1-1a practice - miller...

1-1A Practice Name ______________________________

Date _______________________________

© Addison-Wesley Publishing Company, Inc. AWSM Focus on Advanced Algebra 1

For each scatter plot, tell whether there is a positive association, a negative association, or noassociation.

1. 2.

State whether you believe there is a positive association, a negative association, or no associationbetween each pair of quantities. Explain your reasoning.

3. the perimeter of a square and the area of the square

4. a student’s shirt size and his or her grade point average

5. the average winter temperature in a city and the amount of energy used for heating in that city

6. the age of a computer and the value of the computer

7. The table lists the number of assault crimes committed in one midwestern town.

Year 1983 1984 1985 1986 1989 1990 1991 1992 1993 1994

# Crimes 25 23 30 26 28 34 35 33 37 42

a. Make a scatter plot of the data.

b. Draw a trend line for the data. What type of association do you observe?

c. Predict the number of assault crimes in 1995.

d. The data for 1987 and 1988 were destroyed in a fire.Estimate the number of assault crimes in

1987 and 1988 1984 1986 1988 1990 1992 1994

20

30

10

40

Year

Cri

mes

1-1B Practice Name ______________________________

Date _______________________________

2 AWSM Focus on Advanced Algebra © Addison-Wesley Publishing Company, Inc.

Complete each table. Then write and graph an equation relating x and y.

1. x 0 1 2 3 4 5 2. x 0 1 2 3 4 5

y –3 –1.5 0 1.5 y 4 2 0 –2

Equation Equation

y5

x50

y5

x50

3. Maria’s car can travel 32 miles on one gallon of gasoline.

a. Write an equation relating g, the number of gallons of gasoline in Maria’s tank, and m, the number of miles that Maria can travel.

b. Which variable is independent?

Which variable is dependent?

c. Use your equation to predict how far Maria can travel if she has 7 gallons of gasoline.

4. Toby works at Mighty Mart and earns $7.50 per hour.

a. Write an equation relating p, the amount of Toby’s paycheck, and h, the number of hours thatToby works.

b. How much will Toby earn if he works 20 hours?

c. Toby is hoping that his wages will be raised to $8.25 per hour. Write an equation relating the amount of Toby’s paycheck to the number of hours he works, if he gets the raise.

d. If Toby gets the raise, how much more money will he earn for doing 20 hours of work than hewould earn at his current rate of pay?

Make a table of values for each equation. Include at least 6 entries.

5. y = 3x – 2 6. y = –2x + 5

x x

y y

7. y = 3 – x2 8. y = 12x + 1

x x

y y

1-1C Practice Name ______________________________

Date _______________________________


Tell whether each relationship is a function. If it is, state its domain and range.

1. {(0, 2), (1, 4), (1, 2), (2, 3), (3, –2)}

2. {(–1, 4), (0, 2), (1, 4), (2, 3)}

3. f(x) = (x – 3)2

4. names of students in your math class (independent variable) and the grades they received in amath class at the end of last year (dependent variable)

5. 6.

y5

x50

y5

x50

7. Grover’s Grocery Store has found that the profit (P) from selling one type of canned soupdepends on the price (s). From sales data, the model is P(c) = –100(c – 1.5)2 + 95. Find thestore’s profit on this type of soup for each price.

a. $0.50 b. $1.25

c. $1.50 d. $1.65

e. Explain what a negative value of the profit function represents.

f. What price do you think Grover’s Grocery Store should charge?

Why?

8. Let f(x) = 2x2 + x – 5. Find each of the following.

a. f(–3) b. f(0)

c. f(1) d. f(4)

9. Let g(x) = x + 4 . Find each of the following.

a. g(–6) b. g(–4)

c. g(–2) d. g(0)

1-1D Practice Name ______________________________

Date _______________________________


State whether you believe there is a positive association, a negative association, or no associationbetween each pair of quantities. Explain your reasoning.

1. the speed of travel and the time it takes to travel from Bakersfield to Fresno

2. the day of the month and the number of newspapers sold

3. Complete the table below. Then write and graph an equationrelating x and y.

x 0 1 2 3 4 5

y 2 1.5 1 0.5

y5

x50

Tell whether each relationship is a function. If it is, state its domain and range.

4. the graph shown at the right

5. {(–1, 3), (0, 2), (0, –1), (1, 5)}

6. y = √x – 9

y5

x50

7. Leroy is driving at a rate of 32 miles per hour.

a. If Leroy drives for 15 minutes, how far will he have gone?

b. Write an equation relating t, the number of hours that Leroy drives, and d, the number of

miles he travels.

c. Which variable is the independent variable? the dependent variable?

d. How long will Leroy have to drive in order to travel 224 miles?

1-2A Practice Name ______________________________

Date _______________________________


List the sample space for each situation.

1. two flips of a coin

2. choosing a diagonal of pentagon ABCDE

3. choosing a day of the week

Give the number of outcomes in each sample space.

4. the set of cards in a 52-card deck

5. the set of days in April

6. the set of letters in “sample”

Give the number of outcomes in each event.

7. a day of the week begins with T

8. a 4 is drawn from a standard deck of cards

9. a day in February 1995 is Saturday

10. A standard deck of playing cards includes 13 cards of each suit (clubs, diamonds, hearts, andspades). Each suit includes an ace, jack, queen, king, and the numbers 2 through 10. Find thetheoretical probability that drawing one card from a standard deck results in each event.Express each answer as a fraction.

a. you draw a queen b. you draw a club

c. you draw the ace of spades d. you draw an even-numbered card

11. A bag contains 3 red, 5 blue, 7 green, and 12 yellow marbles. One marble is chosen at random.Find the probability of each of the following.

a. the marble is red b. the marble is yellow

c. the marble is red or green d. the marble is not blue

12. Steve rolls a die 120 times and gets 15 ones and 22 twos. Find the experimental probability ofeach of the following.

a. a one b. a two

c. a one or a two d. neither a one nor a two

1-2B Practice Name ______________________________

Date _______________________________


Describe an appropriate way to model each situation.

1. 70% of the students at Myopian High School wear eyeglasses.

2. 23 of the population of a midwestern town watched last night’s city council meeting on cable

television.

3. About half of Holly’s relatives enjoy bowling.

4. Last winter, it snowed on 20% of the days in one eastern town.

a. Assume that the days when snow falls occur randomly. Use the random digits at the right to estimate the probability that it snows exactly 1 day in a week. (Hint: Let the digits 0 and 1 represent days with snowfall.)

b. Do you think snowfall actually occurs on “random” days?

Explain your answer.

7127240 78496295639530 59478151542693 28612095665310 89949492798022 4984509

Ivan enjoys playing chess. Last year, he won 56 of his games. Today, if he

wins two out of three games, he will win the state tournament.

5. The random digits at the right represent rolls of a die. Use the digits to simulate Ivan playing 15 sets of 3 games. Explain your method.

234 656 151136 156 215451 663 615432 362 411141 556 331

6. Use your results to estimate the following probabilities.

a. Ivan wins at least two games and wins the tournament.

b. Ivan wins only one game.

c. Ivan loses all three games.

7. Do you think Ivan’s probability of winning each game will actually be 56 in this situation?

Explain.

Annette was running out of time on her multiple-choice test, so she had to guess the answers to the lastthree questions. The probability that Annette had a correct answer to any of these questions is 25%.

8. Explain how you can use two coins to simulate the answer to one question.

9. Complete 15 trials of 3 “questions” each, and record your results.

10. Use your results to estimate the probability that she correctly answered.

a. all three questions b. exactly 2 questions

c. exactly one question d. none of the questions

1-2C Practice Name ______________________________

Date _______________________________


Give the number of possible outcomes in each event.

1. a toss of a six-sided die

2. a random digit is odd

3. a month of the year begins with the letter M

4. A card was drawn at random from a deck 75 times and queens turned up 5 times.

What is the experimental probability of drawing a queen from the deck?

5. A set of cards consists of 28 cards. The cards are numbered from 1 to 7 in each of four colors,blue, green, red, and yellow. Give the probability of choosing:

a. a blue card b. a 3

c. an even number d. a yellow 7

e. a green or yellow card f. a number greater than 5

6. Six 3 in. by 5 in. cards are placed in a row on a 2 ft by 4 ft tabletop. A fly lands on a random spot

on the table. What is the probability that the fly lands on one of the cards?

7. About 23 of the students in Barbara’s high school went to the same intermediate

school as she did. Three students at Barbara’s high school are chosen atrandom. Use the string of random digits from 1 to 6 at the right to find theapproximate probability that exactly two of the students went to Barbara’sintermediate school.

Explain your results.

231 523 125311 543 616662 126 565321 512 534212 465 311615 632 554436 461 223

8. Honest Al examined 20 cars on his used car lot and noticed that 16 of the cars had radiosinstalled. Based on this test, if a customer chooses a car at random for a test drive, what is theprobability that the car has a radio?

1-3A Practice Name ______________________________

Date _______________________________


If your answers do not fit on this page, use the back of this worksheet or another sheet of paper.

Use the matrices below to find each of the following, if possible. If not possible, explain why.

A =−2 4

7 −3

3 4

, B =

1 −1 3 2

4 −3 −2 0

, C =

3 −1

5 3

−2 4

, D =

2 1 0 −3

2 5 −3 1

1. A + C 2. D – B

3. 2A 4. 2A – C

5. –B 6. 3D – 2B

7. Find the dimensions of matrix B above.

8. The vertices of a triangle are represented by the columns of the matrix G =−2 1 2

−1 2 −2

.

Graph these vertices and sketch the triangle. Perform each transformation to G and sketch thetransformed triangle. Then use the language of transformations to describe the results.

a. Add T = −3 −3 −3

2 2 2

.

b. Multiply G by 2.

y5

x50

9. The Super Three Ice Cream Company sells vanilla, chocolate, and strawberry ice cream inregular, waffle, or cinnamon cones. The first matrix lists the sales for a Saturday in February, thesecond matrix lists the sales for a Saturday in April, and the third matrix lists the sales for aSaturday in June.

February

V C SReg.

Waffle

Cinn.

43 23 54

23 43 33

28 56 32

April

V C SReg.

Waffle

Cinn.

45 53 45

65 23 54

33 45 65

June

V C SReg.

Waffle

Cinn.

76 56 98

73 81 65

36 65 70

a. Find a matrix showing the change in sales from February to April.

b. Find a matrix giving the total sales in February and April.

c. What was the most popular combination of ice cream and cone sold on the Saturday in June?

d. The owner hopes that the sales in July will be at least twice the combined sales for February and April. Make a matrix showing what the owner hopes to sell in July.

1-3B Practice Name ______________________________

Date _______________________________



Complete each matrix multiplication.

1.−2 3

1 −2

×3 1

0 −1

=−2 ⋅3 + 3 ⋅ ⋅1 + 3(−1)

⋅3 + (−2) ⋅ 0 1⋅ + (−2)(−1)

=

2.

3 2

−2 4

1 −3

×−2 2

3 1

=3 ⋅ + 2 ⋅3 ⋅ 2 + 2 ⋅1

⋅ (−2) + 4 ⋅3 −2 ⋅ 2 + ⋅

⋅ + (−3) ⋅3 ⋅ + (−3) ⋅1

=

Decide if AB exists. If it does, find the dimensions of AB.

3. A is an 8 3 3 matrix and B is a 5 3 8 matrix.

4. A is a 5 3 4 matrix and B is a 4 3 3 matrix.

Use the matrices below to find each product matrix, if possible. If not possible, explain why.

S =1 4

−2 5

2 −1

, T =

3 0 −1

−4 2 5

, U =

3 2 1

−1 2 4

5 2 −2

5. TU = 6. ST =

7. US = 8. SU =

9. TS = 10. UT =

Check whether each pair of matrices is a pair of inverse matrices.

A =3 4

5 7

, B =

7 −5

−4 3

, C =

7 −4

−5 3

11. A and B 12. B and C

13. A and C

14. The tables show the sales and prices for the three top-selling items at Gizmo World.

Sales Price per Item

Gadget Widget Doohickey Gadget $5.99

July 45 34 54 Widget $7.99

August 63 24 64 Doohickey $9.99

September 35 34 65

October 24 75 25

a. Write a matrix for each table. b. Find the matrix product.

c. What does the product matrix represent?

1-3C Practice Name ______________________________

Date _______________________________



1. Find the value of entry D23 in matrix D =

1 2 −4

3 7 −2

−4 3 −1

.

2. Multiply the matrix D above by the 3 3 3 identity matrix. Show your work. Use the matricesbelow to find each of the following, if possible. If not possible, explain why.

E =2 4 −1

4 −4 3

, F =

−2 5 −2

3 6 −2

4 3 −2

, G =

−2 2

6 −4

1 2

, H =

2 4 −3

−1 −1 4

3 2 5

3. F + H 4. G – E

5. 3E 6. H – F

7. 4F – 2H 8. EF

9. FG 10. GH

11. HF 12. GE – H

13. The number of hours worked during the last four weeks and the hourly wages of a smallcompany’s part-time employees are shown below.

Andy Bob Chen Duc Eva Employee Wages ($)

Week 1 15 20 10 8 12 Andy 6.50

Week 2 14 21 30 5 10 Bob 8.50

Week 3 16 18 15 7 11 Chen 9.00

Week 4 18 25 30 10 15 Duc 5.00

Eva 7.50

a. Write a matrix for each table.

b. Use matrix multiplication to show the total amount of wages that the company paid topart-time employees during each of the last four weeks.

2-1A Practice Name ______________________________

Date _______________________________


Find the slope of each line.

1. line l

2. line m

3. line n

4. the line through the origin and (–2, 5)

5. the line through (–4, 3) and (2, 7)

y5

x5

l

m

n0

6. A pyramid is 425 feet along each side of its square base. The peak of the pyramid, located abovethe center of the square base, is 325 feet high. Find the positive slope of the sides of the pyramid.

Decide whether each function is linear. If it is, give its slope and state whether it represents directvariation.

7. f(x) = 25x 8. y = 3x2

9. y – 3 = 4x 10. 3y = 2x

11. f(x) = 2x – 3 12. y2 = 2x + 5

13. 14.

x 2 3 4 5 6 x –1 0 1 2 3

f(x) 4 6 8 10 12 g(x) 5 8 11 15 18

15. Orlando works in telephone sales. He is paid a daily wage of $20plus a commission of $2.00 for every sale he makes. Let P(x) behis gross pay for a day in which he makes x sales.

Write an expression for P(x).

Graph y = P(x). Is P(x) a linear function?

Does y vary directly with x?

16. A set of stairs is constructed with a step tread of 15 inches and a step riser of 9 inches.

What is the slope of the stairway?

2-1B Practice Name ______________________________

Date _______________________________


Solve each equation. Check your solution.

1. 2x – 8 = 5x + 4 2. 3x – 12 = 27

3. 4x + 3 = 9x – 12 4. 8 – 37k = 38 + k

5. 1.3(y + 3) = 0.3(y – 2) + 14.5 6. 3(m – 5) = 3m + 10

7. –6.5a – 8 = 11 + 3a 8. 2(5a – 2) + 3(4 – 7a) = –25

9. 3(2 – z) = 52(2z – 20) 10. 4(8 – 2y) = –8y + 32

11. 12p – 8 = –4p 12. 3(2 – k) = 4k + 13

13.x + 5

7 = 11 – x 14. 4(y – 4) = 2(y + 2)

15. 3j – 18 = –6j 16. 1.8t + 5 = 2.4t – 10

17. Which equations are equivalent to 3x – 5 = 25?

(a) 3x = 20 (b) 3x = 30 (c) x = 10 (d) 30 – 5 = 25

18. Which equations are equivalent to 2x + 8 = 10?

(a) x + 4 = 5 (b) 2x = 18 (c) 2x = 2 (d) x = 1

19. A spice mixture costs 25¢ for the first ounce and 15¢ for each additional ounce. Jeff wants toknow how much he can buy for $4.00.

a. Write a function that relates the cost of the spices in dollars (c) and the number of additional ounces (a).

b. Use the function to write an equation for finding the number of additional ounces he would need to buy in order for the spices to cost $4.00.

Solve the equation.

c. How many ounces can Jeff buy?

20. Alicia is a real estate agent. Her portion of the sales commission is 1.5% of the selling price ofeach property she sells. She wants to know the value of the property she must sell in order to earn$30,000 this year.

a. Write a function that relates the value of the property sold (v) to Alicia’s income (a).

b. Write an equation to determine when her income is $30,000.

c. Solve the equation.

2-1C Practice Name ______________________________

Date _______________________________


Give an equation for each line.

1. with slope = 3 through (2, 9)

2. containing (3, 1) and (5, 2)

3. containing (–2, 6) and (2, 0)

4. containing the origin and (–3, –5)

5. containing (10, 17) and having a y-intercept of 22

6. containing (–2, 4) and having a y-intercept of 8

7. through (2, 3) and parallel to y = 52x + 10

8. through (0, 5) and parallel to y = –2.17x + 3.82

9. through (–2, 7) and perpendicular to y = 25x – 3

10. through (4, 6) and perpendicular to y = –2x + 5

11. the horizontal line containing (2, –4)

12. the vertical line through (–3, 7)

Give the equation of each line.

13.

y5

x50

14.

y5

x50

15. Mr. Takahashi is driving to Oklahoma City at a constant speed. Let t represent the number ofhours that have passed since he started out. At t = 2, he sees a sign that says it is 235 miles toOklahoma City. At t = 3

12, the distance is 160 miles.

a. Express the distance (d) as a linear function of t.

b. What was the distance to Oklahoma City when Mr. Takahashi started out?

c. How fast is Mr. Takahashi driving?

d. When will Mr. Takahashi reach Oklahoma City?

2-1D Practice Name ______________________________

Date _______________________________


Decide whether each function is linear and whether it represents direct variation. If it is linear, give theslope.

1. y = 4x 2. y = 3x2 – 5

3. y + 3 = –2x – 6 4. 3y + 2 = –2x + 5

5. Shelley has started a new business. She had 45 clients two months after she started, and she had75 clients five months after she started. What is the slope between these “points” if you think ofthe number of clients as a function of the number of months in business?

Interpret the slope.

Find the slope of each line containing the following points.

6. (3, 7) and (7, –1) 7. (–5, –8) and (–2, 4)

Indicate the slope and y-intercepts for each equation. Then sketch its graph.

8. y = –2x + 2 9. y = 23x – 3

slope y-intercept slope y-intercept

y5

x50

y5

x50

Solve each equation.

10. 3x – 5 = 16 11. 2p + 5 = 7p – 20

12. 3(k – 2) + 5(k + 3) = 25 13. 17 – 3y = 29

14. Johannes earns $5.50 per hour at his job in the fast food industry, but he has to spend $10.00 eachweek for transportation to and from work. How many hours must Johannes work next week if hewants to have $100, after his transportation expenses? (Ignore taxes)

Find an equation for each line.

15. with slope = 2 through (3, 5)

16. through points (2, –3) and (5, –2)

17. parallel to y = 3x – 2 through (–1, 7)

18. perpendicular to y = –2x + 7 through (2, 5)

2-2A Practice Name ______________________________

Date _______________________________


Write an equation of the trend line for each scatter plot. Use your equation to predict the value of y forthe given value of x.

1. equation

x = 6; y =

y10

x100

2. equation

x = 4; y =

y10

x10

For each set of data, make a scatter plot, draw a trend line, and write its equation.

3. (3, 7), (4, 6), (5, 5), (7, 3),(8, 2), (6, 4), (3, 6), (6, 3)

equation

y10

x10

4. (5, 6), (6, 7), (2, 3), (7, 7),(3, 3), (1, 2), (4, 4), (8, 8)

equation

y10

x10

5. The manager of a telemarketing company recorded figures for the number of hours (h) eachemployee worked per day and the number of sales (s) that employee made. The (h, s) data forseveral employees over several days were:(8, 17), (4, 8), (5, 12), (7, 14), (8, 15), (7, 16), (5, 10), (7, 13), (3, 7), (8, 14)

a. Draw a scatter plot and trend line for the data.

b. Find the equation of your trend line.

c. Use your equation to predict the number of sales that an

employee could produce in 6 hours.

2-2B Practice Name ______________________________

Date _______________________________


Complete the table to show how many points would be in each group when finding three medianpoints of the data.

Number of Data Points First Group (A) Second Group (B) Third Group (C)

1. 27

2. 22

3. 35

Find the coordinates of the centroid of each triangle.

4.

10

10

5

5

y

x

5.

20

20

10

10

y

x

6. Find the equation of the median-median line for the setof data: (5, 6), (3, 3), (5, 5), (2, 3), (6, 6), (4, 5) and(7, 8).

a. List the first, second, and third group of points for determining the median-median line.

first

second

third

b. What are the coordinates of the three median points?

y10

x10

c. What are the coordinates of the centroid of the resulting triangle?

d. Find the slope of the line containing the first and third median points.

e. Write the equation of the median-median line.

Plot this line on your graph.

2-2C Practice Name ______________________________

Date _______________________________


Describe data that each person could model with a line of best fit. Tell what predictions could be madeusing the line.

1. a restaurant owner

2. a school drama coach

3. a school nurse

Use a graphing utility.

4. x 2.3 3.7 5.0 6.3 7.4 8.3 9.5

y 6.3 8.5 4.2 5.6 3.1 2.9 1.5

a. Find the equations of the regression line and the median-median line for these data.

regression

median-median

b. Make a scatter plot of the data and graph both equations.

c. Use each equation to predict the value of y when x = 8.

regression

median-median

y10

x10

5. Mrs. Valdez polled her students and recorded this information.

Hours studied 0 1 112

2 2 212

3 312

4

Grade on test 65 70 75 85 80 80 95 85 90

a. Find the equation of the regression line for the data.

b. Make a scatter plot of the data and graph the equation.

c. Use the equation to predict the score of a student who studied 13

4 hours.

d. Jaime studied 8 hours. Do you think the equation can be used to predict Jaime’s score?

Explain.

2-2D Practice Name ______________________________

Date _______________________________


1. Write an equation of the trend line for the scatter plot.

2. Do the data show positive association, negative

association, or no association?

3. Explain how the association of the data and the slope of

the trend line are related.

4. Based on the equation of the trend line, what value of y

do you expect to get for an x-value of 18?

0

y50

x20

5. Find the coordinates of the centroid of a triangle if the vertices are at (3, 7), (5, 8), and (4, 15).

6. Plot the points (6, 5), (4, 5), (8, 4), (9, 3), (4, 7), (2, 6),and (7, 5).

a. What are the coordinates of the three median points?

b. What are the coordinates of the centroid of

the resulting triangle?

y10

x10

c. Find the slope of the line containing the first and third median points.

d. Write the equation of the median-median line. Plot this line on your graph.

7. Use a graphing utility

x 2.7 3.2 4.0 5.2 5.8 6.3 7.2 7.8 8.4 9.1

y 3.7 4.2 4.6 5.3 4.9 5.8 5.7 6.4 7.0 6.8

a. Find the equation of the regression line for these

data.

b. Make a scatter plot of the data and graph the

equation.

c. Use the equation to predict the value of y when x = 7.

y10

x10

2-3A Practice Name ______________________________

Date _______________________________


Solve and graph each inequality.

1. t – 5 # –3 2124 23 22 0 1 2 3 4

2. –k $ 1 2124 23 22 0 1 2 3 4

3. 3s < 2 2124 23 22 0 1 2 3 4

4.14x + 2 > 3

2

2124 23 22 0 1 2 3 4

5. p – 1 # 2p 2124 23 22 0 1 2 3 4

6. 3(4 – y) + y < 10 2124 23 22 0 1 2 3 4

Write an inequality to match each graph.

7.

2124 23 22 0 1 2 3 4

8.

2124 23 22 0 1 2 3 4

9. A worker earns a base salary of $240 per week plus $9 per hour of overtime. What amounts ofovertime would give the worker a weekly income of $285 or more?

Solve and graph each compound inequality.

10. x + 5 # 5 or x – 3 $ –1 2124 23 22 0 1 2 3 4

11. x – 3 > –6 and 5x < 0 2124 23 22 0 1 2 3 4

12. 13a > 1 or –a > –1

2124 23 22 0 1 2 3 4

13. –2k + 5 $ 11 or 12k $ 1

2124 23 22 0 1 2 3 4

14. –p # 1 and 3p – 5 # 7 2124 23 22 0 1 2 3 4

15. x – 5 > –4 and –2 # –2x + 4 2124 23 22 0 1 2 3 4

16. –5y + 2 $ 7 or 5y – 2 > 18 2124 23 22 0 1 2 3 4

Write a compound inequality to match each graph.

17.

2124 23 22 0 1 2 3 4

18.

2124 23 22 0 1 2 3 4

19. A factory manufactures 2600 cans of soup per day, and no more than 12% of the cans are allowed

to be defective. Describe the acceptable number of defective cans that may be produced in oneday.

2-3B Practice Name ______________________________

Date _______________________________


Evaluate each absolute value.

1. 3 2. −25 3. 0.3

Solve and graph each equation.

4. 2(2x −1) = 2 2124 23 22 0 1 2 3 4

5. 2x −1 = 1 2124 23 22 0 1 2 3 4

6. 3x = 2 2124 23 22 0 1 2 3 4

7. 2 − x = 1 2124 23 22 0 1 2 3 4

8. x + 2 − 5 = −4 2124 23 22 0 1 2 3 4

9. 3x +10 = 13 2124 23 22 0 1 2 3 4

10. Which of the following represents the possible values of the heights of students in Stephanie’sclass if the shortest student is 52 in. tall and the tallest student is 70 in. tall?

(a) 70 − h ≤ 18 (b) h − 61 ≤ 9 (c) h − 9 ≥ 52

(d) h − 61 ≥ 9 (e) not here


11. y − 3 ≤ 1 2124 23 22 0 1 2 3 4

12. 2 p + 2 ≥ 3 2124 23 22 0 1 2 3 4

13. 12 1+ a < 1

2124 23 22 0 1 2 3 4

14. 3(t −1) > 1 2124 23 22 0 1 2 3 4

15. 6 j − 3 ≥ 12 2124 23 22 0 1 2 3 4

16. x −1 − 3 < 0 2124 23 22 0 1 2 3 4

Write an absolute value equation or inequality for each graph.

17.

2124 23 22 0 1 2 3 4

18.

2124 23 22 0 1 2 3 4

19.

2124 23 22 0 1 2 3 4

20.

2124 23 22 0 1 2 3 4

2-3C Practice Name ______________________________

Date _______________________________


Write the inequality for each graph.

1.

y5

x50

2.

y5

x50

Graph each linear inequality.

3. y > 12x + 3 4. y # –2x – 1

y5

x50

y5

x50

Graph each inequality.

5. y < x + 3 −1 6. y ≥ 2 − x

y5

x50

y5

x50

7. Luther’s goal is to drink juice containing 1000 units of vitamin C per day. Brand X contains 600units per cup, Brand Y contains 300 units per cup. Write a linear inequality that shows thecombinations of Brand X and Brand Y that would allow Luther to meet his goal.

2-3D Practice Name ______________________________

Date _______________________________



1. x + 5 > 7 2124 23 22 0 1 2 3 4

2. –3x $ 3 2124 23 22 0 1 2 3 4

3. x – 3 # –5 or 2x + 3 $ 5 2124 23 22 0 1 2 3 4

4. –t < 1 and –2t + 3 > –3 2124 23 22 0 1 2 3 4

5. 2y – 5 < y – 8 or y + 1 $ 0 2124 23 22 0 1 2 3 4

6. 5c – 8 > –8 and –2c + 4 $ 1 2124 23 22 0 1 2 3 4

Solve and graph each absolute value equation or inequality.

7. 5x = 8 2124 23 22 0 1 2 3 4

8. x − 2 = 1 2124 23 22 0 1 2 3 4

9. 4 x +1 = 2 2124 23 22 0 1 2 3 4

10. 2 x −1 ≥ 3 2124 23 22 0 1 2 3 4

11. x + 2 −1 < 1 2124 23 22 0 1 2 3 4

12. x + 5 ≤ −3 2124 23 22 0 1 2 3 4

13. A book is to be made with a height of 8 in. within a tolerance of 14 in. Write an absolute value

inequality that expresses the acceptable heights.

14. Apples cost 35¢ per pound and bananas cost 15¢ per pound. Write a linear inequality thatexpresses the number of pounds of each fruit that Anh can buy if he only has $2.00 to spend.

Graph each linear inequality.

15. y > 23x – 3 16. y # –1

3x + 2

y5

x50

y5

x50

3-1A Practice Name ______________________________

Date _______________________________


Solve each system of equations by graphing if possible.

1. y = 2x + 1

y = –x + 4

y5

x50

2. y = 12x + 1

y = 32x – 3

y5

x50

3. 2x + 3y = 3x + y = 0

y5

x50

4. y = 4x2x – y = –1

y5

x50

5. x + 2y = 23x + y = –4

y5

x50

6. y = 3x – 4y = –2x + 1

y5

x50

7. George needs to send a package to Maryland. Federal Package charges a base fee of $8 plus anadditional $2 per pound. United Shipping charges a base fee of $13 plus an additional $1 perpound.

a. For what weight of package would the charges for the two companies be equal?

b. George’s package weighs 7 pounds. Which service will be cheaper for him to use?

3-1B Practice Name ______________________________

Date _______________________________


Solve each linear system if possible. State the number of solutions, and tell whether the system isconsistent or inconsistent.

1. 3x + y = 7 2. x = 2y – 3

2x – y = –2 4x – 5y = –3

3.25x – 3

5y = –2 4. 4x – y = 9

2x – 3y = 4 –2x + y = –5

5. 3x – 4y = 7 6. x = 2y

y = 2x – 3 –2x + 8y = 16

7. 2x + 6y = 16 8. x + y = 12

3x + 4y = 9 3x – 5y = –4

9. 37x –

57y = 3 10. 2x + 7y = 10

2x + 5y = –11 6x + 21y = 30

11. A chemist has a 20% solution (by volume) of hydrochloric acid and a 35% solution ofhydrochloric acid. He needs to know how much of each to mix together to obtain 600 ml of a25% hydrochloric acid solution. Let x be the number of ml of the 20% solution and let y be thenumber of ml of the 35% solution.

a. Write two linear equations that will determine x and y.

b. Solve the system of equations and describe how the chemist should proceed.

12. Broccoli costs 85¢ per pound and carrots cost 35¢ per pound. Naseem bought 7 pounds ofbroccoli and carrots for $3.45.

How much of each vegetable did he buy?

13. The Chain Gang’s bicycles are available to rent for $12 plus $2 per day. Bicycles from WackyWheels rent for $5 plus $3 per day.

a. For each bicycle, write a function expressing the cost as a function of the number of days

rented.

b. For what number of days will the rental charge be the same for both bicycles.

3-1C Practice Name ______________________________

Date _______________________________


Write each system in AX = B form, where A is the coefficient matrix, X is the variable matrix, and B isthe constant matrix.

1. x + 2y = 6 2. 2x – y = –1

x – 2y = 12 5x – 3y = –1

3. x + 2y = 1 4. 2x + 3y = –2

–2x + y = –7 –3x – 5y = 2

5. x – y = 1 6. 3x – 8y = –9

4x – 5y = 1 2x – 5y = –5

The matrices in Exercises 7–12 are the inverses of the coefficient matrices for Exercises 1-6,respectively. With these inverses, solve the systems of equations in Exercises 1–6 using matrices.

7.12

12

14 − 1

4

8.3 −1

5 −2

9.15 − 2

525

15

10.5 3

−3 −2

11.5 −1

4 −1

12.−5 8

−2 3

Write a matrix equation to represent each of the following situations. Do not solve.

13. Julian bought 9 cans of Super X soup and 3 cans of Mighty Y soup, and he spent $4.50.Katherine spent $2.30 for 4 cans of Super X soup and 2 cans of Mighty Y soup.

Find the price of each can of soup.

14. Roberto drove for 6 hours to get to Fresno, a distance of 318 miles from his home. For the firstpart of the trip (x hours), he drove at 48 mi/hr. For the rest of the trip (y hours), he drove at 60mi/hr.

Find x and y.

15. Use a Graphing Utility. Solve Exercise 13 using matrices.

16. Use a Graphing Utility. Solve Exercise 14 using matrices.

3-1D Practice Name ______________________________

Date _______________________________


Solve each system of linear equations if possible.

1. x – y = –1 2. 2x + z = 7

y + z = 1 x + y + z = 0

3x + 2y + z = 10 2x + 3y – 2z = –8

3. x + y – z = 3 4. 3x – y + 2z = 20

2x – y + z = 5 3x + y – 2z = 4

x – 2y = 4 x + 2y + z = 3

5. x – z = –3 6. x + 2y – z = 5

x – y + 2z = 6 3x – 2y + 5z = 31

2x + 3y – z = 7 –x + 2y – z = –5

7. Find the measures of the three angles of a triangle if the sum of twice the measure of the firstangle and three times the measure of the second angle equals the measure of the third angle, andif the measure of the second angle is 38 more than the measure of the first angle.

8. Yesterday three customers at Kay’s Market bought dates, endives, and/or figs, as shown in thetable. Find the price per pound of each item.

Dates Endives Figs Total

Customer 1 2 lb 1 lb 0 lb $3.85



Write each system of linear equations as a matrix equation in the form AX = B. Then use a graphingutility to solve each system of linear equations using matrices if possible.

9. 2x + 4y + 3z = 6 10. 5x – 2y + 3z = 4

4x – 2y + z = 4 –2x + 4y + 6z = 3

–x + 3y + 4z = –2 8x + 7y – 3z = –6

11. 2x – 3y + z = 4 12. 3.5x + 2.2y – 2.7z = 4.3

–5x + 2y + 3z = –3 4.3x – 1.8y + 2.3z = 2.538x + 7

4y +

34z = 6 3.6x + 1.3y + 5.3z = 2.9

3-1E Practice Name ______________________________

Date _______________________________


1. Which system of equations has a unique solution?

(a) 2x + 5y = 10 (b) 2x + 5y = 10 (c) 2x + 5y = 10 (d) 2x + 5y = 102x + 5y = –3 2x – 5y = –3 4x + 10y = 20 y = –2

5x + 2

2. Identify the inconsistent system in Exercise 1.

Solve each linear system if possible. State the number of solutions, and tell whether the system isconsistent or inconsistent.

3. x = y – 7 4. 2x + 3y = –92x + y = 1 –4x – 3y = 3

5. 3x + 7y = 23 6. 2x + 3y = 5–4x + 3y = –6 6y = 10 – 4x

7. 2x – 6y = 22 8. y = 2x + 33x – 5y = 13 y = 2x – 5

9. At a gas station, regular unleaded gasoline is 87 octane (87% octane), mid-grade unleaded is 89octane, and premium unleaded is 92 octane. Ronald believes that it will be cheaper to mix regularunleaded and premium unleaded than to use the mid-grade pump. How much regular unleadedand premium unleaded gasoline should be pumped in order to obtain 15 gallons of a mixturewhich has 89 octane?

Write each system in AX = B form, where A is the coefficient matrix, X is the variable matrix, and B isthe constant matrix. Then use the inverse of the coefficient matrix to solve the system of equationsusing matrices.

10. 3x – 2y = –4–7x + 5y = 3 matrix equation

A−1 =5 2

7 3

solution

11. 2x – 5y – 3z = 2x – 3y – z = 5–2x + 6y + 3z = –2 matrix equation

A−1 =3 3 4

1 0 1

0 2 1

solution

12. Roadside Veggie Mart sells asparagus, broccoli, and cabbage. The sales for three days last weekare shown in the table.

Asparagus Broccoli Cabbage Total

Monday 50 lb 25 lb 60 lb $155

Tuesday 65 lb 25 lb 60 lb $185

Wednesday 45 lb 30 lb 50 lb $145

Find the price per pound for each item.

3-2A Practice Name ______________________________

Date _______________________________


Graph each inequality on a coordinate plane.

1. y ≥ 2x − 2

y5

x50

2. 3x + 2y < 6

y5

x50

Write an inequality to describe each situation.

3. Maria cannot spend more than $300.

4. Jose’ needs to buy at least five notebooks.

Graph each system of linear inequalities.

5. y > 12x – 2, y < –2

3x + 1

y5

x50

6. x ≥ 0 , y ≥ 0 , x + y ≤ 4

y5

x50

7. An airplane has two rooms, X and Y, for baggage storage. Themaximum allowable baggage is 2000 pounds, and the baggagestored in room X can weigh no more than 2

3 of the weight of the

baggage in room Y.

a. Write two inequalities to express the facts given above.

b. Write any other inequalities that apply to this situation.

c. Sketch a graph of the region that satisfies all of your inequalities in a and b.

3-2B Practice Name ______________________________

Date _______________________________


Graph the feasible region for each of the following sets of constraints (inequalities). Then find thecoordinates of the vertices.

1. y ≥ 13 x − 2 , y ≤ 2x + 3, y ≤ − 4

3 x + 3vertices

y5

x50

2. x ≥ −3, y ≥ −2, 2x + y ≤ 6, 2y − x ≤ 7vertices

y5

x50

3. x ≥ 0 , y ≥ 0 , y ≤ − 47 x + 7 , y ≤ −3x + 24

vertices

4. x ≥ 0 , y ≥ 0 , y ≤ − 14 x + 40, y ≥ 3

2 x − 30vertices

Write a set of linear inequalities to model the constraints in each situation. Then graph the feasibleregion and find the coordinates of its vertices.

5. A restaurant has 25 tables. Some of thetables (x) are reserved, and the rest areavailable for walk-in customers. Therestaurant never reserves more than 15tables.|inequalities vertices

6. Red marbles cost 15¢ and turquoise onescost 25¢. Jimbo has $1.75 to spend on redand turquoise marbles, and he will buy atmost 5 red marbles.inequalities vertices

3-2C Practice Name ______________________________

Date _______________________________


Write the objective function for each situation.

1. A grocery store makes a profit of 5¢ per pound on bananas and 20¢ per pound on papayas. Thestore wants to maximize profits.

2. A fast food outlet buys ground beef for 90¢ per pound and textured vegetable protein for 60¢ perpound. The outlet wants to minimize costs.

3. You can buy compact discs for $15 and cassettes for $8. You want to maximize the number ofdifferent titles you can buy.

4. Jason has two employers, X and Y. X pays him $5.00 per hour and Y pays him $7.00 per hour.Jason must work at least 5 hours per week for X, and no more than 15 hours per week for Y. Hecan work a maximum of 25 hours total per week.

a. Write a set of linear inequalities to model the constraints in this situation.

b. Graph the feasible region and find the coordinates of its vertices.

c. Jason wishes to maximize his income. Write the objective function.

d. Find the optimal solution. How many hours should Jason work for each employer?

e. How much can Jason earn per week?

5. A health food store wishes to prepare a supply of a special granolaby mixing two existing granolas. The mixture is to contain at most18 pounds of oats and at most 10 pounds of nuts.

Oats Nuts

Amazin’ Oats 40% 10%

Nutty Surprise 30% 35%

a. Let x represent the number of pounds of Amazin’ Oats and let y represent the number of pounds of Nutty Surprise. Write a set of linear inequalities to model the constraints in this situation.


c. The store wants to produce as many pounds of the mixture as possible. Write the objective function.

d. Find the optimal solution.

How much of each kind of granola should the store use?

e. How much of the special granola can the store make?

3-2D Practice Name ______________________________

Date _______________________________


Graph each system of linear inequalities.

1. y ≤ 3x + 4, y ≤ − 12 x +1

y5

x50

2. x + 2y < 4, x − 3y ≥ −1

y5

x50

Graph the feasible region for each of the following sets of constraints. Then find the coordinates of thevertices.

3. x ≥ 0, y ≥ 0, 2x + y ≤ 8

Vertices:

4. x ≥ 2, y ≥ 0, 3x + 4y ≤ 24

Vertices:

5. Mrs. Johnson is buying Halloween candy. A bag of 30chocolate pieces costs 50¢ and a bag of 6 peppermint pieces

costs 25¢. Mrs. Johnson wants at least 35 of the bags of candy to

be chocolate, and the most that she is willing to spend is $4.00.

a. Let x be the number of bags of chocolate candy, and let y bethe number of bags of peppermint candy. Write a set of inequalities to model the constraints for this situation.


c. Mrs. Johnson wants to maximize the number of pieces of candy she buys.

Write the objective function.

d. Find the optimal solution.

How many bags of each kind of candy should she buy?

e. How many pieces of candy will she have?

4-1A Practice Name ______________________________

Date _______________________________


1. Graph the sequence on the coordinate plane. Decide whether itis an arithmetic sequence. If so, give the common differenceand the next term in the sequence. 9, 7, 5, 3, 1, ...

arithmetic sequence?

d a6

10

50n

an

Decide whether the sequence graphed is an arithmetic sequence. If so, give the first term and thecommon difference.

2. arithmetic sequence? 3. arithmetic sequence?

a1 d a1 d

10

10n

an

0

5

50

an

n

Give a formula for the nth term of each arithmetic sequence.

4. 2, 5, 8, 11, 14, ... 5. 14, 2, –10, –22, –34, ...

6. –4, –175

, –145

, –115

, –85, ... 7. 8, 7.25, 6.5, 5.75, 5, ...

8. Give two arithmetic means between –21 and 35.

9. Mr. Velasquez received a salary of $23,000 during his first year at his job.Every year he receives a $1500 raise.

a. Write a formula for an, the salary for the nth year on the job.

b. What is Mr. Velasquez’s salary during his 7th year?

c. During what year will the salary be $44,000?

4-1B Practice Name ______________________________

Date _______________________________


Give the sum of each arithmetic series.

1. 3 + 5 + 7 + ... + 23 2. 42 + 37 + 32 + ... + (–3)

3. (–24) + (–21) + (–18) + ... + 300 4. 6.38 + 6.57 + 6.76 + ... + 11.51

5. 8 + 17 + 26 + ... + 71 6. 47 +

87

+ 127

+ ... + 8

7. Give the partial sum S15 of the arithmetic series 5 + 10 + 15 + 20 + ....

8. Give the partial sum S88 of the arithmetic series 97 + 91 + 85 + 79 + ....

Give each sum.

9. 2nn=1

23

∑ 10. (4n − 2)n=1

10

∑

11. (8n −17)n=1

40

∑ 12. (7n + 3)n=1

18

∑

13. 79 n + 2

3( )n=1

24

∑ 14. 34 n + 13

4( )n=1

16

∑

Write each arithmetic series in sigma notation and find its sum.

15. 7 + 14 + 21 + ... + 77 16. 22 + 19 + 16 + ... + (–23)

17. 3.8 + 9.0 + 14.2 + ... + 128.6 18. 107 + 101 + 95 + ... + (–85)

19. Find the 24th octagonal number, which is equal to S24 for the arithmetic series

1 + 7 + 13 + 19 + ....

20. At Joe’s Cafe, the price of the lunch special increases 25¢ every month. During Joe’s first month

of operation, the price was $3.00.

a. Give the cost of the lunch special during Joe’s 20th month of operation.

b. Suppose that you went to Joe’s for the lunch special once a month for the first 20 months

Joe’s Cafe was in business. Excluding tax and tips, how much would you have spent at Joe’s

Cafe?

4-1C Practice Name ______________________________

Date _______________________________


Decide whether each sequence is an arithmetic sequence. If so, give the common difference.

1. 100, 94, 88, 82, ... 2. 3, 6, 10, 15, ...

3.

10

5n

an

0

4.

10

5n

an

0

5. The first two terms in an arithmetic sequence are 42 and 38.

a. Find the next three terms in the sequence.

b. Find the first four partial sums of the sequence.

6. Insert five arithmetic means between 138 and 180.

7. Write the series 7 + 12 + 17 + ... + 302 using sigma notation and find its sum.

8. Give the 18th partial sum of the arithmetic series 83 + 79 + 75 + 71 + ...

Give the sum of each arithmetic series.

9. 5 + 2 + (–1) + ... + (–82) 10. 267 + 284 + 301 + ... + 692

11. 4n − 9n=1

18

∑ 12. 3n + 2n=1

12

∑

13. the series that has 25 terms and ends ... + 12 + 23 + 34

14. Muffins by Mail charges a set price per muffin plus a flat fee for shipping and handling.The total charge for one muffin is $3.50 and the total charge for a dozen muffins is $11.75.

a. Give the per-muffin price.

b. Give the shipping and handling fee.

c. Give the total charge for 100 muffins.

4-2A Practice Name ______________________________

Date _______________________________


Tell whether each sequence is geometric. If so, give the common ratio and the next term in thesequence.

1. 1, 2, 6, 24, ... 2. –4, 4, –4, 4, ...

3. 2, 4, 6, 8, ... 4. 5, –53, 5

9, –

527, ...

5.

10

5n

an

0

6.

10

5n

an

0

Give a formula for the nth term of each geometric sequence.

7. 3, –6, 12, –24, ... 8. 100, 20, 4, 45, ...

9. 7, –14, 28, –56, ... 10. –3, 3, –3, 3, ...

11. 640, 320, 160, 80, ... 12. 27, 36, 48, 64 ...

Find the positive geometric mean of each pair of numbers.

13. 24 and 1176 14. 300 and 12

15. 100 and 144 16. 81 and 441

17. 25 and 64 18. –10 and –40

19. The 7th term of a geometric sequence with common ratio 14 is 32.

a. Give the first term of the sequence.

b. Give the formula for the nth term.

20. On Tuesday, the first day of a flu epidemic, seven students at Birch High School were absent.Throughout the week, absences mounted geometrically, peaking at 189 on Friday.

Estimate how many students were absent on Wednesday and Thursday.

21. Give the eighth term of the geometric sequence 5, 15, 45, ... .

4-2B Practice Name ______________________________

Date _______________________________


Give each sum.

1. the first 10 terms of 6 + 12 + 24 + ...

2. the first 13 terms of 32 + 16 + 8 + ...

3. 4 + 20 + 100 + ... + 62,500

4. 10,000 + (–1000) + 100 + ... + 0.000001

5. S7 for the series 2 + 8 + 32 + ...

6. S8 for the series 1 + 1.1 + 1.21 + ...

7. 3 15( )n

n=1

5

∑ 8. 24(0.95)n−1

n=1

5

∑

9. 7n−1

n=1

10

∑ 10. 200 25( )n

n=1

7

∑

Write each geometric series in sigma notation and find its sum.

11. 4 + (–12) + 36 + ... + (–78,732)

12. 81,000 + 27,000 + 9000 + ... + 100027

13. 240 + 360 + 540 + ... + 182212

14. 256 + (–192) + 144 + ... + 45916

15. 7 + 28 + 112 + ... + 114,688

16. 70 + (–7) + 0.7 + ... + 0.0000007

17. the first 8 terms of the series 7 – 28 + 112 – 448 + ...

18. Give the first term of the seven-term geometric series that has a common ratio of 3 and a sum of

4372.

19. The sum of a geometric series is 75,938. The common ratio is 35 and the last term is 1458. Give

the first term.

20. A ball thrown from ground-level to a height of 64 feet rebounds to three-fourths of its previoushigh point after each bounce. Find the total distance the ball has traveled when it hits the groundthe sixth time.

4-2C Practice Name ______________________________

Date _______________________________


Determine whether each geometric series converges.

1. 300 + 100 + 3313 + 111

9 + ... 2. 1 –

23 + 4

9 – 8

27 + ...

3. 4 + (–4) + 4 + (–4) + ... 4. 1 – 2 + 4 – 8 + ...

5. 25 + 2.5 + 0.25 + 0.025 + ... 6. 35 –

925 + 27

125 –

81625

+ ...

7. 1 – 1.1 + 1.21 – 1.331 + ... 8. 500 + 300 + 180 + 108 + ...

Give the sum of each infinite geometric series.

9. 1 – 34 + 9

16 – ... 10. 125 + 25 + 5 + ...

11. 200 + 160 + 128 + ... 12. –10 – 7.5 – 5.625 – ...

13. –81 + 27 – 9 + ... 14. 7 + 5 + 257 + ...

15. 15 + 457

+ 13549

+ ... 16. 37 + 3.7 + 0.37 + ...

Write each infinite geometric series using sigma notation and find its sum.

17. 1 + 0.9 + 0.81 + ... 18. 64 + 24 + 9 + ...

19. 10 – 8 + 625 – ... 20. 256 – 64 + 16 – ...

21. 375 + 225 + 135 + ... 22. 1 + 38 +

964 + ...

23. 2000 – 1200 + 720 – ... 24. 1 + 13 + 1

9 + ...

Write each repeating decimal as a geometric series and find a fractional equivalent.

25. 0.6 26. 2.2

27. 0.54 28. 3.535

29. 0.891 30. 0.627

31. A ball is thrown from ground level to a height of 125 feet. It rebounds to 35 of its previous high

point after each bounce. Find the total distance the ball travels before stopping.

32. A ball tossed vertically 100 inches begins a series of bounces. If the ball travels a total of 320inches before stopping, at what height does it rebound after its first bounce?

33. An equilateral triangle has area 128 cm2. A second triangle is drawn by joining the midpoints ofthe sides of the first. A third triangle is then drawn by joining the midpoints of the sides of thesecond. If this process is continued without end, what will be the sum of the areas of all thetriangles? (Count only the central triangle at each stage.)

4-2D Practice Name ______________________________

Date _______________________________


Tell whether each series is geometric. If so, give the common ratio and the formula for an.

1. 3, –6, 12, –24, ... 2. 1000, 200, 40, 8, ...

3. The first two terms of a sequence are 64 and 96.

a. Write the first five terms of the sequence if it is arithmetic.

b. Write the first five terms of the sequence if it is geometric.

c. Find the first four partial sums of the geometric series.

Give each sum.

4. 75 + 15 + 3 + ... + 3

625 5. 7 – 21 + 63 – ... + 413,343

6. S5 for the series 4 – 3 + 94 – 27

16 + ... 7. S10 for the series 5 + 10 + 20 + ...

8. 9(4)n

n=1

6

∑ 9. 12500 45( )n−1

n=1

6

∑

10. 243 + 162 + 108 + ... 11. 10 + 6 + 185

...

12. 32 − 12( )n−1

n=1

∞∑ 13. 45 − 1

3( )n

n=1

∞∑

Use sigma notation to write each series.

14. 5 + 35 + 245 + ... + 12,005 15. 343 – 98 + 28 – 8 + ...

16. Express the repeating decimal 0.034 as an infinite geometric series and as a fraction.

17. Debbie invests $2000 in her IRA account on January 1 of each year. The account earns 10%interest compounded annually, so the value of the account at the end of the year is 1.1 times itsvalue at the beginning of the year.

a. Write a three-term geometric series representing the account balance after Debbie makes her

third annual deposit.

b. Use sigma notation to write a geometric series representing the account balance after Debbie

makes her 20th annual deposit.

c. Find the account balance after Debbie makes her 20th annual deposit.

4-3A Practice Name ______________________________

Date _______________________________


Give each real number.

1. the additive inverse of –7.2 2. the multiplicative inverse of 85

Write each word or phrase that correctly completes each statement.

3. The equation 3 ⋅5 = 5 ⋅3 illustrates the property of multiplication.

4. The number 1 is the identity element.

5. The Property of Addition says that if x and y are elements of a fieldthen x + y must also be an element of the field.

Give an example to illustrate each statement.

6. The operation of raising a number to a power is not commutative.

7. The set {0, 1, 2, 3, 4} is not closed under multiplication.

8. The set of integers is not closed under division.

9. In clock arithmetic with the set {0, 1, 2, 3, 4, 5}, we add (©) and multiply (#) numbers and givethe remainder after dividing by 6.

a. Decide whether the set {0, 1, 2, 3, 4, 5} is closed under each operation.

b. Is there an identity element for each operation?

If so, give each identity.

c. Are there inverses for elements using clock addition?

If yes, explain; if not, give counterexamples.

d. Are there inverses for elements using clock multiplication?

If yes, explain; if not, give counterexamples.

e. Is the set {0, 1, 2, 3, 4, 5} with these operations a field?

Explain.

10. Kirstin says that the set of real numbers cannot be a field because the number 0 has nomultiplicative inverse.

Do you agree? Explain.

11. Lloyd used the formula P = 2l + 2w to calculate the perimeter of a rectangle.Rachel used P = 2(l+ w). What axiom(s) assure that Lloyd and Rachel got the same result?

4-3B Practice Name ______________________________

Date _______________________________


Decide whether each square root is rational or irrational. If it is rational, give its value.

1. 418 2. 9

4

3. –√49 4. 3250

Use the Pythagorean Theorem to find the length of the hypotenuse of each right triangle.

Is this length rational or irrational?

5.

6.2

16.8

6.

21.6

28.8

Simplify each expression. Check your work by comparing the decimal equivalent of the initialexpression to your answer.

7. √50 8. √567

9. –√4000 10. 32243


11. 3x2 = 49 12. √ x = 42

13. √5x = 27 14. 16x2 = 49

Simplify each expression.

15. √ 3√ 4√ 5 16. 3√ 5 – 8√ 5

17. 1824

18. √63h + √28h

19. (x + 2)2 20. 25t4

21. A pendulum has length 43 ft 212 in. Calculate the length of time (t) in seconds that it takes the

pendulum to make one complete swing. Use t = 2π L384 , where L is the length of the pendulum

in inches.

4-3C Practice Name ______________________________

Date _______________________________


Express each imaginary number in terms of i.

1. √–3 2. √–1600

3. √–600 4. − 49


5. √–2564 6. √–2

4649

7. √–75 8. √–225

9. (3 + 2i) + (4 – 6i) 10 (6 – 3i) – (4 + 2i)

11. i5 12. –i8

13. (3 + 2i)(6 – 3i) 14. (4 + 2i)(4 – 2i)

15. (7 + 3i)2 16. 4i√–75

17. (2i)3 18. √–4√–9

19. (–7i)(–3i) 20. 4i3 − 3i2 + 7i −1

Give the additive inverse of each complex number.

21. 3 – 2i 22. –4 + i

23. 17i 24. –42i

25. 17 + 15i 26. –4 – 7i

27. Give the voltage in an electric heater if the current is (10 + 2i) amps and the impedance is

(9 – 4i) ohms.

28. The function f(z) = –2z + (2 – 3i) is to be iterated, that is, evaluated repeatedly using each outputvalue or iterate as the next input value.

a. Find f(z) for the initial value z = 3 + 4i.

b. Find f(z) for z equal to the value you obtained for f(z) in a.

c. Find the next two iterates of f(z).

29. The function f(z) = z2 is to be iterated.

a. Find f(z) for the intial value z = 3 – 2i.

b. Find the next two iterates of f (z).

4-3D Practice Name ______________________________

Date _______________________________


1. Give the complex number represented by each point.

a. A

b. B

c. C

d. D

e. E

imaginary5i

real5

AB

CD

E

0

Graph each complex number.

2. –2

3. –4i

4. 4 + i

5. 4 – 2i

6. –3 + 2i

imaginary5i

real50

The complex conjugate of a complex number a + bi is a – bi. Give the complex conjugate of eachnumber.

7. 3 + 7i 8. –2 + 3i

9. –4 – 7i 10. 6 – 5i

Give each absolute value.

11. −7i 12. 12 − 3.5i

13. −5 −12i 14. 15

Add each pair of complex numbers graphically.

15. (2 – 2i) + (–4 – i)

imaginary5i

real50

16. (–3 + i) + (5 + 3i)

imaginary5i

real50

4-3E Practice Name ______________________________

Date _______________________________


Identify each field axiom illustrated.

1. 3 + 7 = 7 + 3

2. −3.25 ⋅5.62 is a real number.

3. 3 ⋅(5 + 8) = (3 ⋅5) + 3.8

4. 17 ⋅1 = 17

Decide whether each set is a field. If not, tell why.

5. {rational numbers}

6. {complex numbers}

7. {–4, –3, –2, –1, 0, 1, 2, 3, 4}

8. {0, 1}

Classify each number as real, imaginary, or complex. A number may fall under several classifications.

9. 3 – 2i 10. √–16

11. –37 12. (4 + 3i)(4 – 3i)


13. √–81 14. 50n2

15. − 4964 16. (3 + 2i)(7 – 5i)

17. (2 + 3i) + (8 + 5i) 18. (6 – 3i) – (–4 + 2i)

19. (3i)5 20. √176 – √891

Find the complex conjugate of each complex number.

21. 7 + 9i 22. –3 + 2i

23. 14i 24. –5 – 8i

25. A right triangle has legs of lengths 48 and 90. Find the length of the hypotenuse.

Is this length rational or irrational?

5-1A Practice Name ______________________________

Date _______________________________


Plot points to graph each quadratic function. For each, find the coordinates of the vertex, the line ofsymmetry, and the maximum or minimum y-value of the function.

1. y = –x2 + 3x

y5

x50

2. y = 2x2 + 4x – 2

y5

x50

Given each pair of reflection image points on a parabola, find the equation of the line of symmetry.

3. (2, 3), (6, 3) 4. (–4, –4), (7, –4)

5. (3.6, –15), (7.8, –15) 6. (12.7, 16.8), (–23.5, 16.8)

Given the vertex (V) of a parabola and a second point (P) on the parabola, find the coordinates of athird point on the parabola.

7. V(0, –5), P(–4, 20) 8. V(1, 7), P(0, 5)

9. V(8, 12), P(13, 3) 10. V(3, 10), P(7, 26)

Give the coordinates of the vertex, the equation of the line of symmetry, and the image point of thelabeled point for each parabola. What is the maximum or minimum y-value of the function that eachrepresents?

11.

y5

x50

12.

y5

x50

Determine whether each function is quadratic. If it is, write its equation in the form y = ax2 + bx + c.

13. y = (x + 3)2 − x2 14. y = (x + 3)(x − 5)

15. y = 2x(x − 5) + 20 16. y = x2(2x + 5)

5-1B Practice Name ______________________________

Date _______________________________


Graph each set of functions on the same set of axes.

1. f(x) = 2x2 and g(x) = –2x2

y5

x50

2. f (x) = 13 x2, g(x) = − 1

3 x2, and h(x) = −x2

y5

x50

Write an equation in the form y = ax2 that contains each point.

3. (1, 7) 4. (2, –8)

5. (3, –18) 6. (–2, 6)

7. (–4, –64) 8. (–5, 10)

Write the equation of each graph. Then write the equation of its reflection with respect to the x-axis.

9.

y5

x50

(3, –3)

10.

y5

x50

(–1.5, 1.35)

11. The kinetic energy of a moving object, in Joules, is K = 12mv2, where m is the mass in kilograms

and v is the speed in meters per second.

a. For a 3-kg object, write the equation in the form K(v) = av2.

b. Without graphing, compare the graph of K(v) to the graph of f(x) = x2.

c. What kinetic energy values correspond to speeds of 1, 2, 4, and 8 m/s?

d. If you want the object to have a kinetic energy of 54 joules, how fast should it be moving?

5-1C Practice Name ______________________________

Date _______________________________


1. Match each function to its graph at the right.

a. y = −(x − 2)2 + 2

b. y = −(x + 2)2 − 2

c. y = −((x + 2)2 − 2)

d. y = −((x − 2)2 + 2)

y5

x5

01 3

42


2. f (x) = −x2 and g(x) = −(x − 3)2 − 2

y5

x50

3. f (x) = 2x2, g(x) = 2x2 − 3, and

h(x) = 2(x + 4)2 − 3

y5

x50

For each quadratic function, find the vertex of its graph and state whether the y-coordinate of thevertex is the maximum or minimum y-value for that function.

4. f (x) = −7x2 5. g(x) = 12 (x − 3)2 + 5

6. h(x) = − 35 (x + 2)2 + 3 7. p(t) = 5

4 (t − 2)2 − 4

8. r(t) = 3(t + 7)2 −17 9. s(t) = − 38 (t − π)2 + 7

8

Write a quadratic function of the form f (x) = a(x − h)2 + k for each parabola.

10. vertex (2, 3), a = 5 11. vertex (–2, 7), a = –3

12. vertex 37 , 4

9( ), a = − 29 13. vertex 7, − 3

2( ) , a = 23

14. vertex (c, d), a = m 15. vertex (3m, 2n), a = p2

Write a sequence of transformations that will produce the graph of each function from the graph ofy = x2.

16. y = (x − 3)2 + 5 17. y = −(x + 2)2

18. y = −(x + 5)2 − 3 19. y = (x + 4)2 +11

20. y = −x2 − 7 21. y = (x − 8)2 −17

5-1D Practice Name ______________________________

Date _______________________________


Complete each equation.

1. x2 – 6x + ______ = (x – 3)2 2. a2 + 4x + ______ = (a + 2)2

3. n2 + ______ + 121 = (n – 11)2 4. b2 + 0.6x + ______ = (b + 0.3)2

5. y2 + 40y + ______ = (y + 20)2 6. z2 + ______ + 6.25 = (z – 2.5)2

7. m2 + ______ + 169 = (m + 13)2 8. d2 + 50d + ______ = (d + 25)2

9. x2 + ______ + 949

= x − 37( )2

10. y2 + 225 y + ______ = y + 11

5( )2

Complete the square to find the vertex and the line of symmetry of the graph of each function. Find themaximum or minimum y-value of each function.

equation vertex line minimum or maximum

11. y = x2 + 8x

12. y = x2 – 10x

13. y = (x + 2)(x – 6)

14. y = x2 + 5x

15. f(x) = x2 + 2x – 7

16. f(x) = x2 – 6x + 12

17. h(x) = 3x2 + 9x

18. g(x) = 4x2 – 64x + 15

19. h = –6t2 + 14t

20. h = − 12 t2 − 8t +12

21. a. A student wrote (x − 2)2 = x2 − 4. Show that this equation is generally incorrect by comparing the graphs

of y = (x − 2)2 and y = x2 + 4.

b. Are there any values of x that make (x − 2)2 = x2 − 4 true? If so, find them and explain your method.

y5

x50

5-1E Practice Name ______________________________

Date _______________________________


Given the vertex (V) of a parabola and a second point (P) on the parabola, find the coordinates of athird point on the parabola.

1. V(3, 7), P(2, 5) 2. V(0, 0), P(–3, 8)

3. V(7, –4), P(3, 6) 4. V(–3, 6), P(5, 5)

5. V(–2, –4), P(–9, 0) 6. V(–2, 3), P(4, –9)

For each quadratic function, find the vertex of its graph and the line of symmetry. Then state whetherthe y-coordinate of the vertex is the maximum or minimum value for that function.

7. y = 5x2 − 21

8. k(x) = −8(x − 7)2 −18

9. g(x) = 3(x + 2)2 − 5

10. h(t) = −5(t − 3)2 + 7


11. f (x) = x2 + 2, g(x) = (x + 2)2 ,

and h(x) = (x + 2)2 − 2

y5

x50

12. f (x) = 12 (x − 3)2 + 2, g(x) = − 1

2 (x − 3)2 + 2,

and h(x) = − 12 (x − 3)2 − 2

y5

x50

Complete the square to find the vertex and the line of symmetry of the graph of each function.Find the maximum or minimum y-value of the function.

13. y = x2 − 4x +15

14. g(x) = 12 x2 + 7x − 3

15. A ball is tossed from a height of 5 ft with an initial vertical velocity of 12 ft/sec. The heightfunction for the ball is h(t) = −16t2 +12t + 5.

a. Complete the square to write the function in the form h(t) = a(t − h)2 + k.

b. How long does it take the ball to reach its maximum height?

c. What is the maximum height the ball reaches?

5-2A Practice Name ______________________________

Date _______________________________


How many zeros does each quadratic function have?

1.

y5

x50

2.

y5

x50

Use the graph of the related function to solve each equation. Estimate answers where necessary.

3. (x − 3)2 = 1

y5

x50

4. 1 = (x + 2)2 − 3

y5

x50

Rewrite each quadratic equation in standard form.

5. 2x(x – 5) = 7 6. 3(x – 1)2 = 5

7. 3x2 − 2x + 5 = 3x + 2 8. 0 = (x − 8)2

9. 0 = (3x − 5)(2x + 3) 10. 15 = x2 − 3x + 7

Graph each quadratic function and estimate its zeros.

11. y = x2 − 2x − 3

y5

x50

12. y = 2x2 + 3x − 3

y5

x50

5-2B Practice Name ______________________________

Date _______________________________


Match each trinomial with its factors.

1. x2 − 7x +10 A. (x + 5)(x + 2)

2. x2 + 3x −10 B. (x + 5)(x – 2)

3. 2x2 + 7x + 5 C. (x – 5)(x + 2)

4. x2 + 7x +10 D. (x – 5)(x – 2)

5. 2x2 +11x + 5 E. (2x + 1)(x + 5)

6. x2 − 3x −10 F. (2x + 5)(x + 1)

Solve each equation using the Principle of Zero Products. If the equation cannot be solved by factoringsay so.

7. x2 + 2x = 0 8. x2 − 6x + 8 = 0

9. x2 + 8x +15 = 0 10. x2 +16 = 10x

11. x2 − 3x − 4 = 0 12. x2 + 21 = 10x

13. x2 −17x + 6 = 0 14. 7x2 +17x + 6 = 0

15. 4x2 + 5 = 9x 16. x2 − 8x − 9 = 0

17. x2 + 7x = 2 18. 13x +10 = 3x2

19. 4x2 + 23x +15 = 0 20. 4x2 + 4x + 3 = 0

Solve each equation. Where necessary, round your answer to the nearest tenth.

21. 2x2 = 98 22. 3x2 − 75 = 0

23. x2 = 0.16 24. 25x2 = 16

25. 3x2 = 25 26. 16x2 = 55

27. A rectangular swimming pool measures 22 ft by 40 ft. A walkway of width w surrounds the pool.The area of the pool with the walkway is 1440 ft2.

Find w.

22 ft

40 ft

w

w

5-2C Practice Name ______________________________

Date _______________________________


Solve each equation. Leave answers in exact form.

1. 2x2 + 5x − 3 = 0 2. x2 + 5x − 2 = 0

3. 2y2 + 3y + 4 = 0 4. 3x2 + 2x + 4 = 0

5. x2 − 2x − 6 = 0 6. m2 − 5m + 3 = 0

Solve each equation. Where necessary, round answers to the nearest hundredth.

7. x2 + 5x −12 = 0 8. y2 −10y + 3 = 0

9. 2x2 − 6x + 3 = 0 10. 4x2 + 2x − 7 = 0

11. 2.7x2 − 3.8x + 0.6 = 0 12. 4.7x2 + 6.3x − 5.9 = 0

13. 7x2 − 3x − 8 = 0 14. 6n2 + 7n +1 = 0

15. x2 + 4x = 480 16. 9w + 7 = 2w2

17. 3x2 = 8x + 5 18. x2 −15 = −5x

19. t4 − 6t2 + 5 = 0 20. u4 + 5u2 + 2 = 0

21. The surface area of a right circular cylinder is given by SA = 2πrh + 2πr2.What is the radius, rounded to the nearest hundredth, of a right circular cylinder of height 7 cm

and surface area 200 cm2?

22. Suppose the height, in feet, of a ball t seconds after it is tossed upward is modeled by thequadratic function h(t) = −16t2 + 50t .

a. At what time or times will the ball be at a height of 15 ft? Round your answer(s) to the nearest

tenth of a second?

b. At what time does the ball hit the ground?

23. The area of a trapezoid is given by A = b1 + b2

2h, where b1 and b2 are the lengths of the bases and

h is the height. The area of this trapezoid is 19.2 cm2.

Find its height and the length of the unknown base.

h

2.5 h

4 cm

5-2D Practice Name ______________________________

Date _______________________________


Complete the table.

1. 2. 3.

Quadratic Function

Number of zeros

Is the Discriminantb2 − 4ac = 0, < 0, or > 0?

Without solving, determine the nature of the roots of each quadratic equation.

4. 3x2 + 5x − 4 = 0 5. x2 + 6x + 9 = 0

6. 2v2 − 3v + 2 = 0 7. z2 + 8z − 6 = 0

8. −3x2 + 2x + 7 = 0 9. 2x2 − 5x + 4 = 0

Find the number of x-intercepts of each function.

10. y = 3x2 + 5x − 2 11. y = 3.7x2 − 2.8x + 0.52

12. y = 3.7x2 − 2.8x + 0.54 13. y = 2.56x2 − 8.64x + 7.29

14. f (x) = 5x2 + 2x −1 15. F(x) = 7x2 + 6x +1

16. Sketch the graph of a quadratic functionthat opens downward and whosediscriminant is negative.

y5

x50

17. Sketch the graph of a quadratic functionwhose discriminant is positive and whosevertex is in the third quadrant.

y5

x50

Use the discriminant to see if the following has at least one real-number answer. If it does not, say soand explain how you can tell. If it does, find the solution.

18. A ball is tossed upward from a height of 1.5 m with an initial vertical velocity of 3 m/sec.

At what time(s) will the ball attain a height of 2 m?

5-2E Practice Name ______________________________

Date _______________________________


Use the graph of the related function to solve each equation. Estimate answers where necessary.If an equation appears to have no real solutions, say so.

1. −2(x + 2)2 + 4 = 2

y5

x50

2. 12 x2 − x − 7

2 = 4

y5

x50

Solve each equation. Where necessary, round your answer to the nearest tenth.Explain your choice of solution technique.

3. x2 + 5x + 4 = 0

4. y2 − 6y + 2 = 0

5. u2 − 3u −10 = 0

6. 2x2 + 3x − 5 = 0

7. 4x2 − 7x + 2 = 0

8. u2 −10u + 21 = 0

9. 3.2x2 + 4.7x + 0.7 = 0

10. 2.3x2 +1.2x − 4.9 = 0

Solve each equation. Leave answers in exact form.

11. 12x2 − x − 6 = 0 12. x2 − 4x +13 = 0

13. 2x2 + 5x − 3 = 0 14. 3x2 + 2x − 5 = 0

15. 2x2 + 3x + 7 = 0 16. x2 + 4x − 8 = 0

Without solving, determine the nature of the roots of each quadratic equation.

17. 3u2 + 7u + 4 = 0 18. 2y2 − 5y + 4 = 0

19. x2 + 2x + 2 = 0 20. 25x2 − 70x + 49 = 0

21. 2z2 − 6z + 7 = 0 22. 4x2 + 2x − 9 = 0

23. The product of two consecutive odd integers is 483. What are the integers?

24. A ball is dropped from a height of 200 m. h t( ) = −4.9t2 + v0t + h0( )a. At what time does the ball have a height of 150 m?

b. At what time does the ball hit the ground?

5-3A Practice Name ______________________________

Date _______________________________


Write an equation for each circle in standard form.

1.

y5

x50

2.

y10

x100

Graph each equation or inequality.

3. (x − 3)2 + (y −1)2 = 4

y5

x50

4. (x + 2)2 + (y −1)2 < 9

y5

x50

Find the distance between each pair of points. Where necessary, round answers to the nearesthundredth.

5. (3, 7) and (–1, 10) 6. (4, –3) and (–5, –9)

7. (–12, 23) and (12, –22) 8. (2, 7) and (15, 21)

Write an equation for each circle in standard form.

9. center (4, 8) and radius 3

10. center (–2, 7) and radius √13

11. center (2, –4) and containing (–3, 7)

Write an equation for each circle in standard form. Then state the center and radius of the circle.

12. x2 + 6x + y2 = 7

13. x2 + y2 +14y = −37

14. x2 − 8x + y2 + 6y = 0

15. x2 +12x + y2 − 6y = −26

5-3B Practice Name ______________________________

Date _______________________________


Graph each ellipse and give the coordinates of its foci.

1. x 2

4 + y2

9 = 1

y5

x50

2. x 2

49 + y2

36 = 1

y5

x50

Write an equation for each ellipse in standard form.

3.

y5

0x

5

4.

y10

x100

Find the eccentricity of each ellipse. Express your answer as a decimal rounded to the nearesthundredth.

5. x 2

25 + y2

9 = 1 6. x 2

144 + y2

169 = 1

By completing the square in x and y, write an equation for each ellipse in standard form.Then give the center of the ellipse.

7. 25x2 −150x +16y2 = 175

8. 4x2 + y2 + 2y = 15

9. 9x2 + 90x +16y2 − 96y = −225

10. 25x2 − 350x + 64y2 + 256y = 119

Solve each equation for y. (Hint: Your equation should have a ± sign.) Then graph each ellipse on agraphing utility. Sketch your result on the back of this page, and state your ranges for x and y.

11. x2

9 + y2

16 = 1 12. 25x2 + 36y2 = 900

5-3C Practice Name ______________________________

Date _______________________________


Graph each hyperbola. Give the coordinates of its foci and the equations for its asymptotes.

1. x 2

4 − y2

9 = 1

y5

x50

2. y2

9 − x 2

25 = 1

y10

x100

Find the differences in the distances from the foci to any point on each hyperbola.

3. x 2

16 − y2

9 = 1 4. y2

25 − x 2

144 = 1

5. x 2

25 − y2

64 = 1 6. y2

81 − x 2

36 = 1

Graph each hyperbola. Give the coordinates of its center and its foci.

7. (x+1)2

9 − (y −1)2 = 1

y5

x50

8. (y−3)2

9 − (x−2)2

16 = 1

y10

x100

By completing the square in x and y, write an equation for each hyperbola in standard form.Then give the center of the hyperbola.

9. 16x2 − 64x − 9y2 = 80

10. 25x2 +100x − 49y2 = 1125

11. y2 − 4x2 − 56x = 212

12. 16y2 + 32y − 49x2 + 392x = 1552

5-3D Practice Name ______________________________

Date _______________________________


Write an equation in standard form for each conic section.

1. a parabola with line of symmetry x = 2 and containing (2, 3) and (4, –5).

2. a circle with center at (3, 7) and containing (–2, 9)

3. an ellipse with foci (0, –4), and (0, 4) and containing (3, 0)

4. a hyperbola with center at the origin, a vertex at (4, 0), and an asymptote with equation y = 34x

State whether the graph of each equation is a circle, an ellipse, a parabola, or a hyperbola. If it is acircle, identify its center and radius; if it is an ellipse, its center and foci; if a parabola, its vertex; and ifa hyperbola, its center and vertices. Then graph each equation.

5. (x + 2)2 + (y −1)2 = 9

y5

x50

6. x 2

4 − (y−1)2

9 = 1

y5

x50

7. y = −(x − 3)2 + 2

y5

x50

8. (x−1)2

16 + y2

25 = 1

y5

x50

By completing the square in x and y, write an equation for each conic section in standard form. Statewhether the conic is a circle, an ellipse, a parabola, or a hyperbola. Then give the center of the conic.

9. y = 3x2 −12x + 7

10. 9x2 − 54x − 4y2 −16y = −29

11. 9x2 +108x + 4y2 − 32y = −244

12. x2 −10x + y2 − 6y = −9

5-4A Practice Name ______________________________

Date _______________________________


Graph and estimate the solutions of each system of equations.

1. y = (x −1)2 − 3y = 1

y5

x50

2. x2 + y2 = 25x + y = 1

y5

x50

3. x 2

16 + y2

9 = 1

y = 43 x + 3

y5

x50

4. y2

16 − x 2

16 = 1

x = 3

y10

x100

Solve each system of equations symbolically.

5. y = x2 + 2x −1 6. 3x2 + 4y2 = 38y = –2x − 5 y = 2x

Graph each system of inequalities.

7. x 2

4 + y2

16 ≤ 1 and y > − 13 x + 2

y5

x50

8. y ≥ (x + 2)2 − 4 and y ≤ 32 x + 2

y5

x50

5-4B Practice Name ______________________________

Date _______________________________



1. y = x2 − 4x + 3 and y = −x2 + 6x − 5

y5

x50

2. (x+1)2

9 + y2

4 = 1 and (x−2)2

9 + (y−2)2

4 = 1y

5

x50

3. x2 + y2 = 25 and y = x2 − 5

y5

x50

4. x 2

4 − y2

9 = 1 and x 2

16 + y2

9 = 1

y5

x50


5. 3x2 + 2y2 = 14 6. y = x2 + 4x + 2

x2 − y2 = 3 y = 12 x2 − 6

7. 3x2 + 2y2 = 21 8. 25y2 − 9x2 = 19

y = 3x2 9x2 − 4y2 = 65


9. y ≥ 2x and x 2

9 + y2

16 > 1

y5

x50

10. x2 + y2 ≤ 16 and y > x2

y5

x50

5-4C Practice Name ______________________________

Date _______________________________



1. y = x2 + 2x − 3 and y = 2x – 2

y5

x50

2. x 2

16 + y2

9 = 1 and y = 32 x − 3

y5

x50

3. x2 + y2 = 4 and x 2

4 + y2

16 = 1

y5

x50

4. y2

4 − x 2

9 = 1 and y = x2 − 2

y5

x50


5. y = x2 + 3x − 2 6. x2 − 3y2 = 4y = 7x – 2 x = –2y

7. x2 + y2 = 64 8. 5x2 − 2y2 = 2y = x2 − 8 x2 + 2y2 = 22


9. y < 12 x + 2 and y ≥ (x − 2)2 −1

y5

x50

10. x2

9 + y2

16 ≤ 1 and x2

16 + y2 ≥ 1

y5

x50

6-1A Practice Name ______________________________

Date _______________________________


Evaluate each expression.

1. 3! 2. 5!

3. 7! 4. 6! – 2!

5. 4! + 5! 6. 8 ⋅ 7!

7. 0! 8. 9! – 4!

9. During your turn in a game, you toss two dice.

a. How many ways can you get a sum of 4?

b. How many ways can you get a sum of 8?

c. How many ways can you get a sum of 4 or 8?

10. You are given a test with five true-false questions and seven multiple-choice questions, each withfour possible answers.

a. How many possible answers are there for each true-false question?

b. How many ways are there to complete the true-false section?

c. How many ways are there to complete the multiple-choice section?

d. Use the Multiplication Counting Principle to find out how many different answer sheets couldbe filled out.

11. At Pasta Panic, you can order spaghetti, fettucini, or angle hair pasta with your choice of pestosauce or marinara sauce.

a. How many types of pasta are there?

b. How many choices of sauce are there?

c. How many ways can you order pasta with sauce?

12. A license plate has three letters followed by three digits.

a. If the letters and digits can be repeated, how many different license plates are possible?

b. If the letters and digits cannot be repeated, how many different license plates are possible?

13. At Robert’s Restaurant, a meal consists ofsoup or salad, a main course, and dessert. Themain course is a choice of quiche, chicken, orfish. Dessert is chocolate cake or strawberrypie. Draw a tree diagram to show and count acustomer’s options for ordering dinner.

6-1B Practice Name ______________________________

Date _______________________________


1. List all 2-letter permutations of the letters in the name RALPH.

2. How many ways can four friends line up in a row for a photograph?

3. List all distinguishable permutations of all letters in the name ROSS.


4. 5P5 5. 5!

6. 7P2 7. 5P3

8. 8P6 9. 12P1

10. How many ways can a president, secretary, and treasurer be elected from a club with 21

members?

11. How many permutations are there of 9 objects taken 5 at a time?

Give the number of distinguishable permutations in each word.

12. WEEKLY 13. SCRABBLE

14. CINCINNATI 15. GEOMETRY

16. MOONSTONE 17. MAMMAL

18. How many permutations of the letters in PRIDE begin with a consonant?

19. How many ways can 3 red, 7 yellow, 4 blue, and 5 green marbles be lined up in a row?

20. How many positive 4-digit odd integers can be formed using the digits 3, 5, 6, 7, 8, and 9:

a. if repetition is allowed? b. if repetition is not allowed?

21. How many different positive 7-digit integers can be formed by rearranging the digits in the

number 4,624,324?

22. A classroom has 15 different books. How many different ways can one book be assigned to each

of 7 students?

6-1C Practice Name ______________________________

Date _______________________________


1. A radio disk jockey needs to play four commercials of the next commercial break. In how manydifferent orders can the commercials be played?

2. An art show has 25 pieces of art on display. In how many possible ways can the first place,second place, third place, and honorable mention ribbons be awarded?

3. How many ways can MORSE be encoded by substituting 5 letters of the alphabet for its letters?


4. 7! 5. 3 ⋅6!

6. 4! + 6! 7. 4!( ) ⋅ 3!( )

8. 5P3 9. 8P5

10. 6P1 11. 7P4

12. At the Salad Emporium, a meal consists of a bowl of soup, a large salad, and a muffin. Threekinds of soup, six kinds of salad, and four kinds of muffin are offered. How many meals areavailable?

13. In a board game, a player begins each turn byspinning a spinner and then tossing a 6-sideddie. The spinner has three congruent sectors, ablue one, a green one, and a red one. Draw atree diagram to illustrate the differentoutcomes that are possible when a player spinsthe spinner and tosses the die. How manyoutcomes are possible?

Give the number of distinguishable permutations of all the letters in each word.

14. NOON 15. DEDICATION

16. DEEPNESS 17. BROCCOLI

18. During your turn in a game, you toss two dice.

a. How many ways can you get a sum of 10?

b. How many ways can you get a sum of 11?

c. How many ways can you get a sum of 12?

d. How many ways can you get a sum that is greater than 9?

19. How many ways can a family of seven line up in a row for a photograph?

20. How many ways can 2 white, 3 purple, and 5 orange marbles be lined up in a row?

6-2A Practice Name ______________________________

Date _______________________________



1. 40C3 2. 20C10

3. 30C1 4. 200C199

5. 35C28 6. 15C8

7. How many ways can you choose three different ice cream scoops from a choice of fifteenflavors?

8. Seven family members got together for a reunion. If each family member hugged each otherfamily member one time, how many hugs took place?

9. A committee of five members needs to be chosen from a 32-member club.How many ways can the committee be chosen?

10. A bag contains 15 different marbles. A collection of six marbles is chosen from the bag.How many ways can the collection be chosen?

11. Rhonda plans to invest $2000 in each of four stocks.How many ways can she choose the four stocks from a list of ten?

12. Five cards are drawn from a deck of 52 cards.What is the probability that all five cards are clubs?

13. Pizza City offers nine different pizza toppings and two choices of pizza crust.How many different 4 toppings pizzas are available?

14. There are nine points on a circle.

a. How many different chords can be drawn by connecting any two of the points?

b. How many different triangles can be inscribed in the circle using any three of the points?

c. How many different pentagons can be inscribed in the circle using any five of the points?

15. A hand of six cards is dealt from a deck of 52 cards.What is the probability that the hand consists of three 5s and three 7s?

16. Mary Jo is taking a test. She needs to answer 7 of the 10 questions.How many ways can she choose which 7 questions to answer?

17. Four students are to be chosen from a class of 25 to show some of their work on the blackboard.How many ways can the students be chosen?

a. if the order is important

b. if the order is not important

6-2B Practice Name ______________________________

Date _______________________________


1. Write the fifth term of the expansion of (x + y)9.

2. Write the fourth term of the expansion (x – y)7.

3. Write the third term of the expansion of (2x + y)8.

4. Write the fourth term of the expansion of (2x – 3y)9.

5. Write the first three terms of (x + y)7.

6. Write the first three terms of (4 – y)8.

Expand each binomial.

7. (x – y)5

8. (x + 3)7

9. (2x – y)8

10. (x – 2y)5

11. (4u – 3v)6

12. (2a + 5b)4

13. (–2t + 3u)5

14. How many terms are in the expansion or (x + y)13?

15. How many terms are in the expansion of (3wx + 4yz)25?

16. One term of (3a + 2b)12 contains a7? What is the exponent of b in that term?

17. There is a 40% chance of rain for each of the next 6 days. The coefficient of xhy6–h in theexpansion of (0.4x + 0.6y)6 gives the probability of exactly h days of rain in the next 6 days.

What is the probability of exactly 4 days of rain?

18. Expand (h + t)6 as a model for flipping a coin six times. The coefficient of hct6–c is the number of

ways to flip c heads in six tosses.

a. What is the total number of outcomes possible from six coin flips?

b. How many of the outcomes have two heads and four tails?

c. What is the probability of getting two heads and four tails?

d. How many of the outcomes have at least four heads?

e. What is the probability of getting at least four heads?

6-2C Practice Name ______________________________

Date _______________________________



1. 10C4 2. 5C3

3. 8C5 4. 12C2

5. 25C25 6. 15C3

7. Monica wants to buy any three of the twelve CDs that are on sale this week at the CD Attic.

How many different ways can she make her selection?

8. You draw 3 cards from a deck of 52 playing cards.

Give the probability that all three cards are diamonds.

9. There are seven points on a circle. How many different triangles can be inscribed in the circle

using any three of the points?

10. A committee of five is to be chosen from a 72-member club.

How many ways can the committee be chosen?

11. A box contains 11 different pieces of chocolate candy.

How many ways can Jimmy choose three pieces to eat?

12. Pancho’s Pizza offers ten different pizza toppings.

How many different ways can Roberta choose one, two, or three toppings for her pizza?

Expand each binomial.

13. (x + y)7

14. (2x – y)6

15. (4a + 3b)5

16. (5c – 7d)6

17. (m + 5n)7

18. (x – 7)6

19. Write the third term of the expansion of (2x + y)11.

20. Write the seventh term of the expansion of (u – v)8.

21. Use the expansion of (0.5 G + 0.5 B)6 to determine the probability that a couple planning to have

six children will have 3 girls and 3 boys.

7-1A Practice Name ______________________________

Date _______________________________


Find each constant of variation.

1. y varies directly with x. y = 60 when x = 15.

2. t varies inversely with x. t = 43 when x =

12.

3. h varies directly with the square of x. h = 20 when x = 2.

4. b varies inversely with the square of a. b = 34 when a =

23.

5. y varies inversely with the square of x. y = 18 when x = 4.

6. n varies directly with m. n = 18 when m = 6.

7. Suppose y varies directly with x. When x = 15, y = 20. Find y when x = 30.

8. Suppose y varies inversely with x. When x = 5, y = 20. Find y = when x = 25.

9. Suppose v varies directly with the square of u. When u = 3, v = 36. Find v when u = 4.

10. Suppose z varies inversely with the square of y. When y = 20, z = 13. Find z when y = 10.

11. Suppose w varies jointly with u and v. When u = 5 and v = 8, w = 80.

Find w when u = 6 and v = 10.

12. Suppose c varies jointly with the square of a and the cube of b. When a = 3 and b = 2, c = 36.

Find c when a = 4 and b = 5.

For each of the following, determine the effect on t when s is doubled.

13. t varies directly with s

14. t varies inversely with the square of s

15. t varies directly with the cube of s

16. t varies inversely with the cube of s

For each equation tell how the dependent variable varies in its relationship with the independentvariables.

17. volume and radius in V = 43pr3

18. Area, length, and width in A = lw.

19. Radius and circumference in r = C2π

20. Distance and time in D = 16t2

21. The kinetic energy (E) of an object varies jointly with the mass (m) of the object and the squareof its velocity (v). An object with mass 2 kg and velocity 3 m/sec has a kinetic energy of 9 Joules.

a. Write a variation equation

b. Solve for the variation constant.

c. Find the kinetic energy of an object with mass 5 kg and velocity 4 m/sec.

7-1B Practice Name ______________________________

Date _______________________________


1. The graph shows sections of the graphs ofy = x4 and y = x6. Which graph is which?

y5

0x

5

2 21 1

Explain.

2. The graph shows sections of the graphs ofy = x8 and y = x9. Which graph is which?

y5

0x

5

2

1

Explain.

Graph each pair of equations on the same set of coordinate axes.

3. y = x2 and y = x3

y5

x50

4. y = x5 and y = x7

y20

x200

If the figure has line symmetry, draw the lines of symmetry; if it has point symmetry, sketch the pointaround which the figure is symmetric.

5. 6.

7. Answer each question to analyze the graph of y = x10.

a. Does the graph resemble a quadratic or cubic curve?

Explain.

b. Does the graph have line symmetry or point symmetry?

Explain.

c. For values of x greater than 1, does the graph appear to rise more steeply or less steeply than the graph of y = x2?

7-1C Practice Name ______________________________

Date _______________________________


Determine if each equation is true or false. If the equation is true, name the property of exponents thatjustifies it. If it is false, change the equation to make it true.

1. 22 ⋅ 23 = 26

2. 35( )4

= 34

54

3. (3 ⋅11)4 = 3 ⋅114

4. (72 )3 = 76

5. 67

64 = 63

6. (32 )4 = 36

Simplify. Write answers with positive exponents.

7. (5x)3 8. (5x)−3

9. t−3 ⋅ t2 ⋅ t0 10. (−4t2 )5

11. (−2x)4 12. (3ab2c3)4

13. x2y5

x4y3 14. (2x3 )3

(3x2 )−1

15. (a0bc2 )−4 16. (−4t3u−2 )−3

17. 27(x2y−3z4 )2

36y 18. 52(u2v5w−3 )−2

68(u−3vw2 )−3

Write each number in standard notation.

19. In chemistry, a mole is 6.02 3 1023 molecules.

20. The speed of light is 3 3 108 m/sec.

21. The mass of the moon is 7.35 3 1022 kg.

Write each number in scientific notation.

22. The mean distance from the earth to the Sun is 150,000,000,000 m.

23. The mean radius of the earth is 6,371,000 m.

24. The orbital period of the sun about the galactic center is about 1,750,000,000,000 hours.

Simplify and write in scientific notation.

25. (3.2 ×105)(2.4 ×10−3) 26. (2.7 ×108)(5.2 ×1012 )

27. 2.7×105

1.8×1012 28. 2.4×10−3

9.6×10−17

29. 6.35 ×104( ) 2.8 ×1021( ) 30. (4.2 ×10−6)3

31. Find the volume of a box with length 3 ×10−5 mi, width 2 ×10−5 mi, and height 4 ×10−5 mi.Write your answer in scientific notation.

7-1D Practice Name ______________________________

Date _______________________________


Give the constant of variation.

1. r varies inversely with p. r = 12 when p = 5.

2. t varies directly with the square of s. t = 45 when s = 3.

3. h varies directly with g. h = 75 when g = 50.

4. Suppose w varies jointly with u and v. When u = 4 and v = 10, w = 30. Find w when u = 14 andv = 6.

5. Suppose z varies inversely with y. When y = 12, z = 8. Find z when y = 4.

6. Suppose q varies directly with the square of p. When p = 5, q = 100. Find q when p = 7.

Graph each pair of equations on the same set of coordinate axes.

7. y = x7 and y = x8

y5

x50

8. y = −x3 and y = x4

y5

x50

Simplify. Write answers with positive exponents.

9. (2d)−3 10. (7c0d2e−4 )2

11. (3x5)2(2x−1)3 12. x2y4

z3

x−1y2

2z−1

2

13. (3.8 ×106) ⋅ (7.2 ×10−21) 14. 2.7×108

5.4 ×10−27

Write each number in scientific notation.

15. 0.000 000 005 23 16. 385,760,000,000

Write each number in standard notation.

17. 2.83 ×108 18. 3.75 ×10−5

19. The travel time varies directly with the distance traveled, and inversely with the average rate.A ship takes 3 hours to travel 27.6 miles at a rate of 8 knots.

a. Write the variation equation. b. Find the constant of variation.

c. Find the length of time a ship takes to travel 69 miles at a rate of 6 knots.

7-2A Practice Name ______________________________

Date _______________________________


If the expression has a fractional exponent, rewrite it using a radical. If the expression has a radical,rewrite it using exponents.

1. 314 2. 7

23

3. 125 4. z53

5. (3 + x)− 3

4 6. (2xy)12

7. (3pq)54 8. x2y33

9. (y2 )57 10. (3ab2 )

23

11. ab3 12. xy2z33

6

If x < 0, tell whether the principal roots for each expression is positive, negative, or does not exist.

13. x4 14. x46

15. x35 16. x23

17. x75 18. x

38


19. 2723 20. 64

− 53

21. 814 22. 3433

23. 1654 24. (−27)

43

25. 8132 26. 25

− 52

27. 873 28. 81

74

Simplify each expresssion.

29. x43

34

30. (p23 )

12

31. (125)23 32. x34

33. 323

343

34. (−2)48

35. x34

5 36. 25

32

−13

37. 612

623

38. 8−1

3

853

7-2B Practice Name ______________________________

Date _______________________________


For each scatter plot, state whether linear regression or power regression models the data more closely.

1.

y

0x

2.

y

0x

Evaluate each expression. Where necessary, round answers to the nearest hundredth.

3. 51.75 4. 063.2

5. 321.2 6. 1−0.37

7. 32.9 8. 4.82−2.3

9. 6.23.8 10. 5.9−0.04


11. x2.3 ⋅ x5.23 12. (y3.6 )4.2

13. p2.9

p−3.8 14. r−2.5

r3.7

15. a2.6b3.2a6.7b0.8 16. (c0.28d2.75)3

17. s2.7

t3.5

10 18. t2.73t8.05

19. Use a Graphing Utility.

a. Graph the following data: (1.3, 2), (2.1, 8), (3.1, 20), (3.9, 35),(4.8, 55), (6.2, 100), (7.1, 135), (8.2, 180)

b. Use power regression to find the function y = AxB that best fitsthe data.

c. Use your function to predict y when x = 4.2.

7-2C Practice Name ______________________________

Date _______________________________



1. x + 6 = 4 2. x − 8 = 3

3. x + 3x + 4 = 8 4. 12 = 2x + 2

5. 4x − 5 = 1 6. 2x + 7 = 7

7. x −12 = 3 + x + 5 8. x + 3 − 8 = 1 − x

9. x −1 + x = 7 10. x + 2 − x = 2

11. 11 − 6x = x −1 12. 8 = 4x

13. 9 = 3x 14. 12 − 3x + 4 = x

15. 6 + x = x 16. 2x + 5 = x − 5

17. x32 = 27 18. x + 13 = −4

19. x12 = 6 20. x

25 = 4

21. 2x + 53 = 3 22. 2x13 + 5 = 9

23. x23 = 25 24. 2 = 2x − 65

Solve for the given variable.

25. x = 72y2, for y 26. t = s, for t

27. x32 = y, for x 28. y = 8

27 x3, for x

29. t = D4 , for D 30. b = 4 ×105 a , for a

31. v = 4u4, for u 32. z = 2 xy3 , for x

33. y = x43 , for x 34. t = s45 , for s

35. If you invest P dollars in an account whose annual yield is r, the amount of money (A) you willhave after n years (assuming you make no other deposits or withdrawals) is A = P(1 + r)n.

a. Solve this equation for r.

b. Suppose you have $1500 to invest, and that you will need that money to grow to $2200 in 5 years. At what yield do you need to invest the money?

36. The volume (V) of a sphere with radius r is given by V = 43 πr3.

a. Solve this equation for r.

b. Find the radius of a sphere with volume 28.5 cm3.

7-2D Practice Name ______________________________

Date _______________________________


Solve each equation by graphing.

1. 2x + x + 4 = 3 2. x + 4 −1 = 2 − x

y5

x50

y5

x50


3. x + 1 + 2x = 7 4. 2 x + 1 = 10 − 2x

5. 8 = x + 9x 6. 7x − 3 = 2 + 4x + 1

7. 5 + x + 1 = 3x 8. 2 = x + 8 − x − 4

State whether each equation is in quadratic form.

9. 2x3 − x2 + x = 0 10. 5x2 − 2x + 1 = 0

11. x8 − 8x4 + 3 = 0 12. 3.8x5 + 2.4x2 − 2 = 0

13. 7.5 x3 − 8.2 x6 − 4.7 = 0 14. 2.7x43 + 3.2x

23 −1.2 = 0


15. x − 3 x − 4 = 0 16. x23 + 7 x3 + 12 = 0

17. x83 + 5 x43 −14 = 0 18. x − 8 x + 15 = 0

19. x32 − 7x

34 + 10 = 0 20. 2x5 + 5 x5 −12 = 0

21. Jorge’s home is located at (3, 7). Kathy’s home is located at (1, –5). If Lee’s home is equidistantfrom Jorge’s house and Kathy’s home, find an equation that represents all possible locations ofLee’s home.

7-2E Practice Name ______________________________

Date _______________________________


Evaluate each expression. Where necessary, round answers to the nearest hundredth.

1. −83 2. 814

3. 2.83.78 4. 25− 1

2

5. 162.5 6. 171.2

7. 2432/5 8. 0.125−8

3


9. x2/3 ⋅ x3/4 10. (x34 )

52

11. a2.38 ⋅ a3.72 12. (z1.73)3

13. x35 14. x106

15. (c2.7d3.8)1.8 16. m3.6n−2.7

m−2.7n−3.2


17. x + 2 = 7 18. 9 = 3x + 21

19. x + 4 − x + 1 = 5 20. 5 = 8 − x + 4

21. x + 6x + 1 = 9 22. 8 + x = −2x + 4

23. 6 − 23 − x = 3 + x 24. 12 − 11x + 5 = 6x + 1

25. x + 3 = 8 − 5x − 5 26. 7 = 2x + 5 + 2 x + 2

27. x4/3 −10x2/3 + 9 = 0 28. x − 2 x − 3 = 0

29. x3 − 8 x3 + 15 = 0 30. x45 − 2x

25 − 8 = 0

31. x + 7 x4 − 8 = 0 32. x65 − 3x

35 −10 = 0

33. The $1750 that Stephanie put in a savings account 8 years ago has grown to $3006.83. Find theinterest rate she has been earning. Use the formula A = P(1 + r)n , where A is the amount in theaccount after n years and P is the principal, the amount initially invested.

34. Solve E = 12 mv2 for v. 35. Solve z = 3x2

y3 for y.

7-3A Practice Name ______________________________

Date _______________________________


Let f(x) = x2 + 1 and g(x) = 2x – 3. Find each value or expression.

1. ( f + g)(3) 2. (f – g)(5)

3. ( f ⋅ g)(4) 4. (g – f)(2)

5. f(t) 6. ( f + g)(a)

For each pair of functions, graph f and g on the same set of axes. Then use your graphs to find thegraph of (f + g)(x).

7. f(x) = 3, g(x) = –(x + 2)2

y5

x50

8. f(x) = 2x – 3, g(x) = –x + 2

y5

x50

For each pair of functions, find (f + g)(x), (f – g)(x), and ( f ⋅ g)(x).

9. f(x) = x + 3, g(x) = –x + 5

10. f(x) = x2, g(x) = 2x

11. f(x) = 3x2 + 5x, g(x) = 2

12. f(x) = 2x – 5, g(x) = 3x + 1

13. f(x) = x2 + 5, g(x) = –2x

14. f(x) = x2 + x, g(x) = 3x – 1

15. The function h is the set of ordered pairs (1, 3), (2, 4), (3, 2), (4, 6), (5, 5), (6, 1).The function k is the set of ordered pairs (1, 5), (2, 3), (3, 6), (4, 4), (5, 7), (6, 2). Find each value.

a. (h + k)(2) b. (h – k)(5)

c. (k – h)(6) d. (h ⋅ k)(3)

e. (h ⋅ k)(5) f. (h + k)(1)

7-3B Practice Name ______________________________

Date _______________________________


Let g(x) = x2 and h(x) = 2x + 1. Find each value or expression.

1. g(–2) 2. h(3)

3. g(h(2)) 4. h(g(–3))

5.

(g o g)(x) 6.

(h o g)(x)

For each pair of functions, find f(g(2)) and g(f(2)).

7. f(x) = 3x – 2, g(x) = x2

8. f(x) = x2 + 1, g(x) = 2x – 5

9. f(x) = x3, g(x) = x2 – 6

10. f (x) = x2 + 2x + 4, g(x) = x −1

11. f(x) = 5x, g(x) = x + 4

12. f(x) = x – 2, g(x) = x3

For each pair of functions, find

(h o k)(x) and (k o h)(x).

13. h(x) = x + 7, k(x) = 2x – 3

14. h(x) = 5x – 8, k(x) = 3x + 5

15. h(x) = x2 + 2x + 1, k(x) = x – 1

16. h(x) = x3, k(x) = x4

17. h(x) = x2 – x, k(x) = x + 2

18. h(x) = 2x + 6, k(x) = 12x – 3

Let f(x) = x + 3, g(x) = x2, and h(x) = 2x – 3. Find each composite function.

19. g(g(x)) 20. f(f(x))

21. f(h(x)) 22. g(f(x))

23. f(g(h(x))) 24. h(f(g(x)))

25. Jaime is blowing up a balloon. Suppose the volume (V), in cm3, of the balloon is given byV = 30t, where t is the time in seconds since he began blowing up the balloon.

a. Find a function giving the radius (r) of the balloon as a function of the volume.

b. Find a function giving the radius of the balloon as a function of time.

c. When will the radius surpass 12 cm?

7-3C Practice Name ______________________________

Date _______________________________


The graph of a relation is shown. Sketch the graph of the inverse relation.

1. y5

0x

5

2. y5

0x

5

Graph each function and its inverse.

3. y = 12x + 2

y5

x50

4. y = x3

y5

x50

For each pair of functions, show that the functions are inverses of each other.

5. f(x) = x + 7, g(x) = x – 7

6. f(x) = 2x + 5, g(x) = 12x –

52

7. f (x) = 3x + 9, g(x) = x − 93

8. f (x) = x + 73 , g(x) = x3 − 7

Find the inverse of each function.

9. f(x) = x – 3 10. f(x) = 4x – 8

11. f(x) = 5x + 20 12. f(x) = (x + 1)3

13. f (x) = 2x5 14. f (x) = x−3

7-3D Practice Name ______________________________

Date _______________________________


Let f(x) = –x2 and g(x) = 2x – 5. Find each value or expression.

1. ( f + g)(4) 2. (f – g)(3)

3. ( f ⋅ g)(−2) 4. (g – f)(–3)

5.

( f o g)(x) 6.

(g o f )(x)

7. ( f + g)(x) 8. (f – g)(x)

9. ( f ⋅ g)(x) 10. (g – f)(x)

For each pair of functions, find h(k(5)) and k(h(5)).

11. h(x) = 5x – 2, k(x) = –2x + 3

12. h(x) = x2 − 8, k(x) = x −1

13. h(x) = 12x + 3, k(x) = 3x – 2

14. h(x) = x3, k(x) = x − 3

For each pair of functions, find f(g(x)) and g(f(x)).

15. f(x) = 3x – 7, g(x) = –3x + 7

16. f(x) = 2x + 8, g(x) = 0.5(x – 2)

17. f (x) = x2, g(x) = 4 − x

18. f (x) = x2 + 6x − 5, g(x) = x − 3

For each pair of functions, show algebraically and graphically that the functions are inverses of oneanother.

19. f(x) = –2x – 3, g(x) = –12x –

32

y5

x50

20. f(x) = x3 + 2, g(x) = x − 23

y5

x50

Find the inverse of each function.

21. f(x) = 3x + 12 22. f(x) = 5 – x

23. f(x) = –12x + 3 24. f(x) = 8x3

25. f (x) = x + 23 26. f (x) = 2 + x3

8-1A Practice Name ______________________________

Date _______________________________


Match each function with its graph. Explain your choice.

1. f (x) = x4 − 3x3 + 2x2 2. f (x) = 12 x3 − 2x

3. f (x) = − 12 x3 + x2 + 2x 4. f (x) = x2 − 4x

A.y

5

0x

5

B.y

5

0x

5

C.y

5

0x

5

D.y

5

0x

5

For each pair of polynomial functions P(x) and A(x), find P + A and P – A.

5. P(x) = x5 − 2x3 + 3x2 + 2x − 5, A(x) = −x4 + 3x3 − 2x2 + 8x − 3(P + A)(x) = (P – A)(x) =

6. P(x) = 2x4 − 3x3 + 5x2 + 8, A(x) = 7x5 + 2x3 − 8x + 2(P + A)(x) = (P – A)(x) =

7. P(x) = 3x3 + 2x2 − 5x + 3, A(x) = 4x3 − 2x2 + 3x − 8(P + A)(x) = (P – A)(x) =

8. P(x) = 4x6 − 3x4 + 2x2 −1, A(x) = 3x4 − 4x3 + 5x2

(P + A)(x) = (P – A)(x) =

Simplify each polynomial, and determine the leading coefficient and degree of the polynomialfunction.

9. f (x) = (x + 4)2 − 6

10. g(x) = x(3x − 2)(x + 3)

11. h(x) = (x + 5)2 − (x − 3)2

12. k(x) = 2(x2 − 3)(x + 4)

8-1B Practice Name ______________________________

Date _______________________________


Use the graph of each function to identify an absolute maximum or minimum if one or both exist.Estimate any additional relative maximums or minimums, and indicate an interval for each.

1. f (x) = x3 − x2 − 4x + 1

absolute maximum

absolute minimum

relative maximums

relative minimums

y5

0x

5

2. f (x) = 12 x4 − 4x2 − 3x + 6

absolute maximum

absolute minimum

relative maximums

relative minimums

y10

0x

5

3. f (x) = 15 x5 + 2

5 x4 − x3 − 65 x2

absolute maximum

absolute minimum

relative maximums

relative minimums

y5

0x

5

4. f (x) = −x4 − x3 + 4x2 + 4x − 3

absolute maximum

absolute minimum

relative maximums

relative minimums

y5

0x

5

8-1C Practice Name ______________________________

Date _______________________________


Find the zeros of each function.

1.

y5

0x

5

2.

y5

0x

5

3.

y10

0x

10

4.

y10

0x

10

Find the zeros of each function. Tell what method you used. Check your answers.

5. f (x) = 2x3 − 2x2 − 24x

6. f (x) = 4x4 − 36x2

7. f (x) = x2 − 3x + 2

8. f (x) = 2x2 + x − 21

9. f (x) = x2 − 5x + 3

10. f (x) = x2 + 6x + 10

11. f (x) = 3x3 − 5x2 + 2x

12. f (x) = x3 + 6x2 + 4x

13. f (x) = 3x2 − 4x + 2

14. f (x) = 2x3 − 5x2 − 3x

8-1D Practice Name ______________________________

Date _______________________________


For each pair of polynomial functions P(x) and A(x), find P + A and P – A.

1. P(x) = 3x4 − 2x3 + x2 − x + 4; A(x) = 3x3 − 2x + 5

(P + A)(x) = (P – A)(x) =

2. P(x) = −4x5 + 6x3 − 2x2 + 5x; A(x) = 2x4 − 5x2 + 2x −1

(P + A)(x) = (P – A)(x) =

Simplify each polynomial, and determine the leading coefficient and degree of the polynomialfunction.

3. f (x) = (x − 3)2 − 9

4. g(x) = 2x(x − 6)(x + 5)

5. h(x) = (x + 3)2 + x2 − 4

Use the graph of each function to identify an absolute maximum or minimum if one or both exist.Estimate any additional relative maximums or minimums, and indicate an interval for each. Then findthe zeros of each function. Approximate your answers when necessary.

6. f (x) = 15 x3 − 2

5 x2 − 115 x + 12

5

y5

0x

5

absolute maximum

absolute minimum

relative maximums

relative minimums

zeros

7. f (x) = x4 −11x3 + 44x2 − 76x + 48

y5

0x

5

absolute maximum

absolute minimum

relative maximums

relative minimums

zeros

Find the zeros of each function.

8. f (x) = x3 + 5x2 −14x 9. g(x) = x3 − 49x

10. h(x) = 2x6 + x5 −15x4 11. k(x) = 2x3 − 6x2 − 3x

8-2A Practice Name ______________________________

Date _______________________________


Sketch the graph of each function. Find the x-intercepts.

1. y = 3x + 2 y

5

x50

2. y = x2 − 5x + 4 y

5

x50

Solve each equation graphically. Estimate the solutions if necessary.

3. x3 + x2 − 6x = −8

4. x3 + x2 − 6x = −4

5. x3 + x2 − 6x = 0

6. x3 + x2 − 6x = 6

y10

0x

10

y = x3 + x2 2 6x

7. − 12 x3 + 1

2 x2 + 5x − 4 = −6

8. − 12 x3 + 1

2 x2 + 5x − 4 = −4

9. − 12 x3 + 1

2 x2 + 5x − 4 = 0

10. − 12 x3 + 1

2 x2 + 5x − 4 = 4

y10

0x

5

y =2 x3 + x2 + 5x 2 412

12

11. x4 − x3 − 4x2 + 4x + 3 = −3

12. x4 − x3 − 4x2 + 4x + 3 = 0

13. x4 − x3 − 4x2 + 4x + 3 = 2

14. x4 − x3 − 4x2 + 4x + 3 = 4

y5

0x

5

y = x4 2 x3 2 4x2 1 4x 1 3

8-2B Practice Name ______________________________

Date _______________________________


Solve each equation by factoring.

1. x3 − 3x2 −10x = 0 2. x3 = 8

3. x3 + 3x2 = 4x 4. x4 = 16

5. x4 − 8x3 + 15x2 = 0 6. x4 −15x2 −16 = 0

7. 4x(x −1) = x3 8. x3 + 3x2 = x + 3

Use division to find each quotient and remainder.

9. (x3 −13x + 12) ÷ (x − 3)

10. (x3 + x2 − x + 13) ÷ (x + 3)

11. (x3 − 2x2 − 21x + 20) ÷ (x − 5)

12. (2x3 −13x2 + 29x −15) ÷ (2x − 3)

13. (x4 − 2x3 − 7x2 + 5x + 6) ÷ (x + 2)

14. (6x3 − x2 − 26x + 19) ÷ (3x + 7)

Find each remainder when the first polynomial is divided by the second polynomial.

15. 2x3 + 4x2 − 3x + 5; x + 3 16. 3x3 − 2x2 + 5x − 7; x − 5

17. 2x4 − 3x3 + x2 − 2x + 7; x − 3 18. 4x9 − 3x5 + 2x3; x −1

19. 2x4 + 7x3 − 3x2 + 4x − 2; x + 1 20. x3 − 4x2 + 2x − 5; x − 2

21. Find a polynomial that has quotient 2x – 7 and remainder 5 when divided by 3x + 2.

22. When polynomial P(x) is divided by x + 3, the quotient is 2x2 + 3x −1 and the remainder is –4.Find the value of P(–3).

23. Explain how you can determine whether x + 2 is a factor of P(x) = 3x4 + 2x3 + 7x −12 withoutactually dividing.

24. Give a polynomial function that has zeros of –1, 0, 3, and 5.

25. Write a polynomial equation with roots 4, 2 – 5i, and 2 + 5i.

26. The length of a box is 3 in. more than twice the width, and the height is 10 in. less than 3 timesthe width. The volume of the box is 720 square inches. Find the dimensions of the box.

width length height

8-2C Practice Name ______________________________

Date _______________________________


Decide whether each polynomial equation has multiple roots. If so, state which roots. Then give thetotal number of roots of the equation, counting multiplicity.

1. (x − 3)(x −1)(x + 2)3 = 0

2. (x2 − 4)(x + 3) = 0

3. x3 − 2x2 − 8x = 0

4. (x −1)2(x − 2)(x − 3)(x2 − 4) = 0

5. (x + 1)(x + 3)(x − 4)(x + 1) = 0

6. (x3 − 4x2 + 2x)(5x3 + 2x2 − x)

7. (x2 + x − 6)(x2 + 8x + 15) = 0

8. (x − 5)(x2 − 25) = 0

9. (x3 + 8)(x3 − 8) = 0

10. (x − 64)(x2 − 64)(x3 − 64) = 0

Find all roots of each polynomial equation.

11. x3 + x2 −17x + 15 = 0

12. x3 + 6x2 + 3x −10 = 0

13. 2x3 −13x2 + 24x − 9 = 0

14. x4 + x3 −15x2 + 23x −10 = 0

15. x4 − 2x3 − 7x2 + 8x + 12 = 0

16. 2x3 + 3x2 −17x + 12 = 0

17. 2x4 − 3x3 + 33x2 − 48x + 16 = 0

18. 3x4 + 5x3 − 29x2 − 45x + 18 = 0

19. 5x4 − 23x3 + 37x2 − 25x + 6 = 0

20. 2x5 + 36x3 −13x4 − 72x2 + 112x − 80 = 0

21. A polynomial has leading coefficient 1 and constant term 10. Find all possible rational roots ofthe related polynomial equation if all coefficients are integers.

22. A polynomial has leading coefficient 5 and constant term 2. Find all possible rational roots of therelated polynomial equation if all coefficients are integers.

8-2D Practice Name ______________________________

Date _______________________________


Solve each equation graphically. Estimate the solutions if necessary.

1. −x3 + 7x2 −12x + 2 = −3

2. −x3 + 7x2 −12x + 2 = 0

3. −x3 + 7x2 −12x + 2 = 2

Use division to find each quotient and remainder.

y5

0x

5

y = 2x3 1 7x2 2 12x 1 2

4. (2x3 + x2 −12x + 7) ÷ (x + 3)

5. (4x3 − 2x2 + 2x + 21) ÷ (2x + 3)

6. (3x4 −13x3 −15x2 + 33x − 43) ÷ (x − 5)

7. (12x4 − 31x3 + 41x2 − 52x + 42) ÷ (3x − 4)

Find the remainder when the first polynomial is divided by the second polynomial.

8. x3 − 2x2 + 5x − 3; x − 3 9. x4 + 2x2 − 6x + 1; x + 2

10. x21 − 3x16 + 5x5; x + 1 11. 5x3 − 2x2 − 6x + 7; x − 3

12. 3x3 + 2x2 + 8x −15; x + 2 13. 2x4 + 7x3 − 5x2 + 3x − 2; x + 4

14. Find a polynomial P(x) that has quotient 3x – 2 and remainder 7 when divided by 4x + 5.

15. What can you say about factors of polynomial R(x) if –3 is a root of the equation R(x) = 0?

16. Give a fifth-degree polynomial equation with roots 3, 6, and 8, and no other roots.

17. A polynomial has leading coefficient 6 and constant term 1. All coefficients are integers.

Find all possible rational roots of the related polynomial equation.


18. x3 + 2x2 −15x = 0 19. x4 − 35x2 − 36 = 0

20. x4 −10x3 + 35x2 − 50x + 24 = 0 21. x4 + 2x3 − 25x2 − 50x = 0

22. 2x3 −17x2 + 41x − 30 = 0

23. x5 − 7x4 − x3 + 55x2 − 84x + 36 = 0

8-3A Practice Name ______________________________

Date _______________________________


Evaluate each rational expression for the given value of the variable.

1. 2x + 53x − 2 for x = 3 2. y2

2y +3 for y = –4

3. 3m − 42m + 5 for m = 6 4. 6t −8

t3 for t = 2

5. 2d − 5−3d + 5 for d = 4 6. k2 + 2

k2 − 4 for k = 5

7. 3x + 27x − 4 for x = –2 8. 4 j −3

2 j + 2 for j = –4

9. x2 − 2x +3

2x2 + 5x for x = 3 10. 2t

3t2 − 4 for t = 1

Divide each pair of complex numbers.

11. 8 4 2i 12. 10i 4 (4 – 3i)

13. (–7 – 19i) 4 (4 + 5i) 14. (16 + 11i) 4 (2 + 3i)

15. (6 + 3i) 4 (4 – 2i) 16. (8 – 2i) 4 (–3 + 4i)

17. (5 + 3i) 4 (2 – 3i) 18. (6 – i) 4 (3 + 5i)


19. −54x5y2

36x2y4 20. 44a6b121ab5

21. 2a2 + a −152a − 5 22. 2x2 − 5x −3

3x2 − 4x −15

23. x3 +3x2 − 4x −12

x2 +3x −10 24. 24x2y3

z4 ÷ 42xz5

y2

25. x2 − 42x +3 ⋅ x2 − x−12

x − 2 26. x − 4

3x2 + x − 2⋅ 3x − 2

x2 − 7x +12

27. y2 − 2y

y2 + y − 20÷ 3y − 6

y2 −3y − 4 28. m + 2

2m2 + 7m + 5÷ m2 − m − 6

2m + 5

29. Let z be the impedance of an electrical component in ohms. The expression 6zz + 6 gives the total

impedance (in ohms) of a 6-ohm resistor connected in parallel with the other electricalcomponent. Give the total impedance of the parallel components for each value of z.

a. z = 8i ohms b. z = –7 – 5i ohms

c. z = 4 ohms d. z = –2 + 3i ohms

8-3B Practice Name ______________________________

Date _______________________________


Find the least common denominator of each pair of rational expressions.

1. 2x +1

5x2 ; 4x − 215x 2. 3u − 2

18u3 ; 4u +3

81u7

3. zz2 − 4

; 152z + 4 4. 6a − 2

a +3 ; 3a −1a −3

5. 2xx2 + 2x −8

; 3x − 7

x2 + x − 6 6. 2v + 5

v2 +3v −18; 2v −10

v2 −36

7. 3c2 −8c4c −12 ; 2c + 5

c2 + 4c − 21 8. 2t +8

t2 +8t +12; 3t

t2 −3t −10

9. 53x2 − 48

; 72x2 + 6x −8

10. w2 +3

2w2 + 7w + 6; 2w

w2 −3w −10


11. 2x + 53x + 4x −3

6x2 12. 3v − 2

5v3 − 2v + 9

4v2

13. 3y − 52y + 2y +3

y2 + 2y 14. 4t − 5

t +3 + 4t + 6t +3

15. 6x −32x + 5 − 2x −13

2x + 5 16. 2ww +3 + 6w

w + 5

17. 1z +3 − 1

z −3 18. x + 4

x2 − x − 6+ 3x − 2

x2 +3x + 2

19. 3a −12a + 6 − 7a

a2 + 7a +12 20. t2 −1

t2 + 7t +10− 2t + 4

t2 − t − 6

21. 3r − 24r +12 + 6r

2r2 + 5r −3 22. 5a + 2

2a +10 − 3a − 43a +15

23. Two rectangles each have an area of 80 in.2, but one rectangle is one inch wider than the other.

a. Let w be the width of the narrower rectangle, and write a rational expression that gives the difference in the lengths of the two rectangles.

b. What is this difference if the narrower rectangle has width 4 inches?

24. A motorboat can travel 25 mi/hr on still water. The boat’s captain is planning a round-trip to adestination 120 miles down river, and the river flows at a rate of x mi/hr.

a. Write the total travel time as a rational expression of x.

b. Evaluate your expression for x = 5.

c. Evaluate your expression for x = 15.

d. Evaluate your expression for x = 30.

Is your result meaningful?

Explain.

8-3C Practice Name ______________________________

Date _______________________________


Determine where any discontinuities will occur in the graph of each rational function.

1. f (x) = 12x − 7 2. g(x) = 2x +3

x2 −16

3. y = 2x + 2

x2 − 2x −3 4. y = x2 + 9

x2 − 5x

5. F(x) = x2 − 7x

2x2 −11x − 21 6. R(x) = 4x

x3 −3x2 −10x

Make a table of values and sketch a graph of each rational function. Describe any discontinuities in thegraph.

7. f (x) = 1x − 2 8. f (x) = x2 +3x −18

2x − 6

x x

y y

y5

x50

y5

x50

9. f (x) = 2x − 6

x2 − x − 6 10. f (x) = −x

x2 + 2x −3

x x

y y

y5

x50

y5

x50

8-3D Practice Name ______________________________

Date _______________________________



1. 12x − 1

3x = 6 2. 3− x6 + 6 = 2 + x

4

3. 4a + 2a + 2 = 2a − 5 4. x

4 + 5x −1 = 4x +1

4

5. 4x − 2 + 4

5 = 222x −1 6. 2z

z − 2 = z − 3

7. c −1c − 4 + c − 2 = 5c − 2

c − 4 8. x2 − x − 6x −3 + x +1 = x2

9. x +5x +3 = x

x − 2 − 10

x2 + x − 6 10. 5

x + 2 + x +18 = 12

x + 2

11. x2 −3x −10

x2 − x − 6= 0 12. x +3

x − 2 + x − 4 = 7x − 2

13. x2 − x − 20x + 4 + x2 = 7 14. x

3 − 4x +1 = x −1

4

15. x − 24 − 3

x −1 = 2x −107 16. 1

x +1 + 32x −3 = x

5

17. 4x +1 + 4 = 15

x 18. x − 29 + 12

x +1 = x − 6

19. 4x + 2 = 2x − 2

9 20. x4 + 3

x +1 = 2x −32

21. If two electrical components with resistances of r1 ohms and r2 ohms are connected in parallel,the total resistance is R, where 1

R = 1r1

+ 1r2

.

a. What resistance can be connected in parallel with a 60-ohm resistor to produce a total resistance of 35 ohms?

b. One resistor has a resistance that is five ohms less than twice the resistance of a second resistor. When the two resistors are connected in parallel, the total resistance is 6 ohms.

Find the resistance of each resistor.

c. One resistor is connected in parallel with another resistor whose resistance is eleven ohms lessthan twice the resistance of the first resistor. The total resistance is sixteen ohms less than the resistance of the first resistor.

Find the resistance of each resistor.

22. A car was driven fifteen miles per hour faster than a bicyclist was traveling. If the car traveled 50miles in the time it took the cyclist to travel 20 miles, what was the speed of each?

8-3E Practice Name ______________________________

Date _______________________________


Evaluate each rational expression for the given value of the variable.

1. x2 + 2x +32x − 5 for x = 5 2. −2r +3

4r −1 for r = –2

3. 56t − 4 for t = 4 4. 3z2

3z + 5 for z = 5


5. x2 − 4x +3x + 2 ⋅ 2x − 5

x2 +3x − 4 6. x −3

2x −3 ⋅ 2x −3

x2 − 9

7. u3 − 5u2 −14u2u − 2 ÷ u2 −u − 6

u2 +3u − 4 8. c −3

c2 −3c −10÷ c2 + c −12

c + 2

9. 3z −8z − 5 + 4z −1

z − 2 10. 2s −1

s2 − 2s −15− 4s

2s2 − 9s − 5

Give the values of x where each function is undefined.

11. f (x) = 2xx2 + 9x +14

12. g(x) = x2 − 5x + 6

x2 + 2x −15

13. h(x) = 5x +1

x2 −3x −10 14. k(x) = x2 −3x − 4

x2 −8x +16

Make a table of values and sketch the graph of each rational function. Describe any discontinuities.

15. f (x) = −3x +1 16. f (x) = x3 − 2x2

x − 2

x x

y y

y5

x50

y5

x50

Solve each rational equation.

17. 3x −1 = x +1

x +3 18. 4x − 2 + 2

x +3 = 1

19. 7x −1 + 8− 4x

x − 2 = x + 42 20. x + 2

6 − 4x +1 = x

7

21. 4x +1 + x +3

6 = 2x5 22. 11

2x2 +3x − 5+ 3

x −1 = 2

9-1A Practice Name ______________________________

Date _______________________________


Let f(x) = 4x−1. Evaluate f(x) for each value of x.

1. f(0) 2. f(1)

3. f(2) 4. f(–3)

5. f(t + 5) 6. f(3v)

Let g(x ) = 13( )x+2

. Evaluate g(x) for each value of x.

7. g(–6) 8. g(–4)

9. g(0) 10. g(1)

11. g(4a) 12. g(z – 5)

Graph each exponential function. Label the coordinates of at least two points on each curve.

13. y = 15( )x

y5

x50

14. y = 3x

y5

x50


15. 2x = 16 16. 3−x = 243

17. 5x = 0.2 18. 64x = 8

19. 8−x = 16 20. 4x = 32

21. 27x = 81 22. 8x = 164

23. 13( )x

= 27 24. 125( )x

= 125

25. A city had a population of 300,000 people in 1987. Its population has been growing at an annualgrowth rate of 7.5%.

a. Let t be the number of years after 1987. Write a function that relates t to the population (P) ofthe city.

b. Estimate the city’s population in 1997.

9-1B Practice Name ______________________________

Date _______________________________


The equation 15,826(1.12)t models the growth in the world production of a certain chemical since1977 (in tons). Use this equation to estimate the production of the chemical in each year.

1. 1979 2. 1983

3. 1987 4. 1995

5. 2005 6. 2020

7. The population of a country increased from 1,273,854 to 1,352,382 from 1970 to 1980.

a. Find the average yearly rate of increase.

b. Let t be the number of years since 1970. Write an equation to model the country’s population.

c. Predict the country’s population in 1987.

8. Property values have been declining in Sue’s neighborhood. Her home was worth $178,000 in1990, but it was worth $156,000 in 1995.

a. Find the average yearly rate of decline.

b Let t be the number of years since 1990. Write an equation to model the value of Sue’s home.

c. If the trend continues, what will Sue’s home be worth in 2002?

9. In one midwestern city, an average two-bedroom apartment rented for $425 in 1980 and for $544in 1990.

a. Find the average yearly rate of increase.

b. Let t be the number of years since 1980. Write an equation to model the average rental rate.

c. Predict the average rental rate in 1997.

Use a graphing utility for the following exercises.

10. A town’s population was 75,000 in 1990. The town’s population has been growing at a rate of2.65% per year. Predict the year when the population will reach 100,000.

11. A chemical has a half-life of 48 minutes. At time t = 0, a sample contains 800 grams of thechemical.

a. Write an equation for the number of grams of the chemical that remain after t minutes.

b. How long does it take the 800 grams to decay to less than 10 grams?

9-1C Practice Name ______________________________

Date _______________________________


State whether a linear or an exponential model is more appropriate for each of the following situations:

1. The local market increases its prices 3% every year.

2. The enrollment of a middle school is increasing 25 students per year.

3. The population of Smalltown is decreasing by one fifth every decade.


4. 5 12( )3 5. 196(1.2)5

6. 3.72(0.95)4 7. 1000(1.08)6

8. The median price of a home in Happy Grove can be approximated by the exponential regressionequation P = 120,000(1.06)t, where t is the number of years since 1980.

a. What is the growth rate of home prices in Happy Grove?

b. Estimate or predict the median price of a home in:

i. 1987 ii. 1992 iii. 2000

9. The graph shows a function that models the population of acounty during 1970-1990. Use the graph to estimate the yearwhen the population was:

a. 400,000

b. 500,000

c. 600,000

d. 700,000

y1000

500

01970 1980

x1990

Popu

latio

n (t

hous

ands

)

Year

Use a graphing utility to make a scatter plot for each set of data. Then find an exponential regressionequation in the form y = abx to model each data set.

10. 11.

x 4 12 23 36 40 45 x 5 25 40 60 70 90

y 5 8 17 48 71 93 y 9.3 5.9 4.0 2.8 2.3 1.4

9-1D Practice Name ______________________________

Date _______________________________


Use the Rule of 70 to estimate each of the following.

1. The doubling time for a savings account that pays 8.5% interest.

2. The interest rate needed so that the value of an investment will double in 11 years.

3. The time it will take a stock price to quadruple if it increases 23% per year.

For each function, find f(x) for x = 0, 1, 3, 6, and 10.

4. f (x) = 3000e0.055x

5. f (x) = 10,000e−0.23x

6. f (x) = 8e0.2x

7. f (x) = 500e−0.05x

Find the value of each investment. Assume interest is compounded continuously.

8. $2000 invested at 5% for 2 years



11. $500 invested at 6.5% for 10 years

12. $700 is deposited in a savings account that pays 10% yearlyinterest.

a. Write and graph a function that shows the growth of the money over the next 10 years, if the interest is compounded continuously.

b. Find the amount that will be in the account after 10 years if the interest is compounded.

i. continuously ii. daily

iii. monthly iv. annually

13. The population of a bacteria culture is given by the equation P(t) = 325,000e0.05t, where t isgiven in hours.

Find the population after:

a. 2 hours b. 8 hours c. 3 days

9-1E Practice Name ______________________________

Date _______________________________


For each function, find f(t) for the values t = 0, 1, 2, 6, and 10.

1. f (t) = 1000 34( )t

2. f (t) = 150(1.09)t

3. f (t) = 2000e0.04t

Graph each exponential function. Label the coordinates of at least two points on the curve.

4. y = 32( )x

y5

x50

5. y = 45( )x

y5

x50


6. 3x = 127 7. 4x = 128

8. 125x = 125 9. 2

3( )x= 81

16

10. A substance has a half-life of 30 minutes. How long will it take 320 grams of the substance todecay to 5 grams?

11. Suppose you deposit $3000 in a bank account earning 8.5% interest. Find the value of theaccount after 7 years if the interest is compounded:

a. annually b. quarterly

c. monthly d. continuously

12. The population of a small town can be approximated by the exponential regression equationP = 6842(1.045)t , where t is the number of years since 1975.

a. What is the annual growth rate of the population of this town?

b. Estimate or predict the population in:

i. 1982 ii. 1993 iii. 2010

9-2A Practice Name ______________________________

Date _______________________________


Graph each logarithmic function. Label the coordinates of at least two points on each curve.

1. y = log2 xy

5

x50

2. y = log1/3 xy

5

x50

3. y = log xy

5

x50

4. y = log3(x + 2)y

5

x50

Rewrite each equation. If it is in exponential form, rewrite it in logarithmic form; if it is in logarithmicform, rewrite it in exponential form.

5. log2 32 = 5 6. log3181 = −4

7. 62 = 36 8. log 10,000 = 5

9. 14( )−3

= 64 10. 53 = 125

Evaluate each expression. If necessary, round answers to the nearest hundredth.

11. log 0.001 12. log3127

13. log5 625 14. ln 1e2

15. log 5.7 16. 3ln 8.25


17. log2 x = 5 18. log3 x = −2

19. logx 36 = 4 20. log0.25 x = 12

21. logx1

512 = 9 22. log5 x = −3

9-2B Practice Name ______________________________

Date _______________________________



1. ex = 5.72 2. 10x = 0.05

3. ex = 127,422 4. 10x = 127,422

5. e5x = 372 6. 10x−3 = 5874

7. 30e0.075t = 55 8. 10x2 −5x+10 = 10,000

9. log 3x = 2.7 10. ln(2x − 5) = 3.78

11. log(5x + 8) = 2.83 12. ln x25( ) = −2

13. Ira has just put $2000 into his retirement account. He hopes that the account will be worth at least$5000 when he retires in 10 years.

a. Suppose that the account pays 8% interest, compounded continuously.

Write an equation to represent this situation.

b. How long will it take before the account has a balance of $5000?

Will the account be worth $5000 when Ira retires?

c. Write an equation to find the interest rate that will give a balance of $5000 in 10 years.

What is the interest rate?

14. You have invested $500 in an account that earns 6.5% interest, compounded continuously. Findthe number of years it takes the $500 to grow to:

a. $750 b. $1000

c. $1500 d. $5000

15. You have invested $800 in a savings account. You make no deposits or withdrawals from theaccount. Your goal is for the account to grow to $2000. Interest is compounded continuously.Find the necessary interest rate to reach your goal in:

a. 4 years b. 9 years

c. 15 years d. 28 years

16. The population of a bacteria culture grows by a factor of 10 every day. At t = 0, the population is5000.

a. Write an equation giving the population after t days.

b. Find t when the population reaches 100,000.

9-2C Practice Name ______________________________

Date _______________________________


Classify each statement as true or false. If a statement is true, explain why it is true.If false, change the statement to make it true.

1. log 4 + log 7 = (log 4)(log 7)

2. log 35 = 3log 5

3. ln a − ln b = ln ab( )

4. elog 5 = 5

Simplify each expression by rewriting as a single logarithm.

5. 5log t 6. log 14 − log 7

7. 4 ln x − 5ln y 8. 3log2 ab + 2 log2 bc − 4 log2 ac

9. 3log 2 − (4 log p − 2 log q) 10. 2(log x − log y) + log z

Rewrite each expression as a sum or difference of logarithms.

11. log(xy2 )4 12. ln 3ac

13. log u2

vw

14. ln 3ab

c2

15. log5(4ax + 4ay) 16. log xy


17. 4 ln x = ln 16 18. 3x = 14

19. 23 = 5(1.08)t 20. log 5 = x − log 2

21. ln x + ln 3.75 = ln 30 22. 4x = 0.08

23. log3 x = 2.5 24. log(x + 3) + log(x − 5) = log 9

Use the change of base rule to evaluate each expression.

25. log5 7 26. log2.8 372

27. log6 0.085 28. log4 30

29. log5 625 30. log15 3.7

9-2D Practice Name ______________________________

Date _______________________________


Graph each logarithmic function. Label the coordinates of at least two points on each curve.

1. f (x) = log0.5 xy

5

x50

2. f (x) = log3(x + 4)y

5

x50

Rewrite each equation. If it is in exponential form, rewrite it in logarithmic form; if it is in logarithmicform, rewrite it in exponential form.

3. 43/2 = 8 4. 103 = 1000

5. log3 243 = 5 6. log36 6 = 12

7. log 0.00001 = –5 8. 45( )−3

= 12564

Evaluate each expression. If necessary, round answers to the nearest hundredth.

9. log8128 10. log71

343

11. log0.04 125 12. log1114,641

13. log 437 14. 5ln 2.73

15. You have invested $1500 in a savings account. Your goal is for the $1500 to grow to $2500.Interest is compounded continuously.

a. How long does it take to reach your goal if the rate is 7.65%?

b. What interest rate do you need in order to reach your goal in six years?

Simplify each expression by writing as a single logarithm.

16. 2 log u − 4 log v 17. log3 + log5 + log8 −1

18. log2(ab) − log2(bc) + log2(cd) 19. 3log x + 2 log y

20. 2 ln( pq) − 3ln(qr) + 4 ln(rs) 21. log(x2 − 2x −15) − log(x + 3)


22. log4 x = 52 23. log 7 + log x = log 35

24. 7x = 4 25. 32 log7 x = log7 125

26. 150e0.09x = 220

27. log(2x2 −11x − 40) − log(x − 8) = 2

10-1A Practice Name ______________________________

Date _______________________________


Use nDEF to find each trigonometric ratio.

1. sin D

2. cos D

3. tan F

4. cos F

5. csc D

6. cot D

D

FE

20

21

29

Use nGHI to find each length or angle measure.

7. g

8. m/G

9. m/H

G

HI g11

61

Use nJKL to find each length or angle measure.

10. j

11. k

12. m/K

K

LJ

j

k

32

518

Give the sine, cosine, tangent, cosecant, secant, and cotangent of each angle measure.

m/A sin A cos A tan A csc A sec A cot A

13. 408

14. 258

15. 328

16. 738

Give the measure of the acute angle with each given value.

17. sin A = 0.3 18. cos B = 0.7

19. tan C = 1.0 20. sin D = 0.5

21. cos E = 0.4 22. tan F = 2.4

23. A 15-ft ladder is placed against a building so that it makes an angle of 288 with the building.

a. At what height, to the nearest foot, does the ladder touch the building?

b. How far from the base of the building is the foot of the ladder?

24. The shadow of a flagpole is 4 ft at the same time that a 5-ft person casts a 1-ft shadow.How tall is the flagpole?

10-1B Practice Name ______________________________

Date _______________________________


Convert each angle measure to radians.

1. 358 2. 728

3. 1258 4. 108

5. 148 6. 398

7. 908 8. 3608

Convert each angle measure to degrees.

9. π4 10. 3π

8

11. 7π12 12. π

3

13. π 14. 2π5

15. 3π10 16. 4π

9

Use a calculator to evaluate each trigonometric ratio of the radian measure.

17. cos π8 18. sin 3π

7

19. tan 2π5 20. cos π

12

21. sin 0.965 22. tan 1.325

23. cos 0.043 24. sin 0.738

Give the exact value of each trigonometric ratio.

25. sec π4 26. csc 458

27. cot 308 28. csc 608

29. A 3313 rpm record makes 331

3 revolutions every minute. Give the number of radians through which

the record turns while playing a 6-minute song.

30. Give the number of radians through which the second hand of a clock turns in 25 seconds.

31. The radius of the earth is 3960 miles. Give the arc distance between two cities which areseparated by a 0.75-radian central angle.

10-1C Practice Name ______________________________

Date _______________________________


The radius of a circle and the measure of a central angle are given. Give the length of the arc that isintercepted by the angle.

1. 14 cm, π4 radians 2. 12 in., 3π

4 radians

3. 3 m, 2.3 radians 4. 7 ft, 358

5. 5 cm, 258 6. 20 in., 3π8 radians

7. 9 m, 0.65 radians 8. 11 ft, 458

Give the area of the sector of the circle with the given radius and central angle.

9. 14 cm, 3π4 radians 10. 18 in., π

10 radians

11. 25 mm, 2π5 radians 12. 10 ft, 4π

9 radians

13. 6 in., 278 14. 10 m, 358

15. 3 cm, 0.95 radians 16. 4 ft, 1.27 radians

17. Ottawa, Ontario, latitude 45.48 N, lies directly north of Philadelphia, Pennsylvania, latitude

39.98 N. Give the distance between Ottawa and Philadelphia.

18. Stockholm, Sweden, latitude 59.38 N, is due north of Cape Town, South Africa, latitude 33.98 S.

Give the distance between the two cities.

19. A lighthouse signal can be seen from distances up to 25 miles away in a 1308 sector.

From what area of the ocean can the lighthouse be seen?

20. A 78-rpm record has a 10-in. radius. Give the linear speed of a point on the edge of the record.

21. Find the angular speed of a 26-in.-diameter bicycle wheel if the bicycle is traveling at a speed of

10 mi/hr.

22. A spinner for a game is divided into eight congruent sectors. Find the area of one of the sectors if

the radius of the spinner is 4 in.

10-1D Practice Name ______________________________

Date _______________________________


For each angle measure, give an equivalent angle measure between 08 and 3608, and tell in whichquadrant the terminal side lies.

1. 4958 2. –5098

3. 12358 4. –258

5. 17π4 6. − 12π

5

7. 28π3 8. 31π

4

A point on the terminal side of an angle of rotation is given. Give the sine, cosine, and tangent of eachangle.

9. (6, –8) sine cosine tangent

10. (24, 7) sine cosine tangent

11. (–15, 8) sine cosine tangent

12. (–60, –11) sine cosine tangent

13. (45, 24) sine cosine tangent

14. (20, –21) sine cosine tangent

15. (–12, –5) sine cosine tangent

16. (–15, 20) sine cosine tangent

Give the value of each trigonometric ratio.

17. cos 1208 18. sin(–608)

19. tan 4958 20. csc 1508

21. sec 11π6 22. cot − 5π

2( )

23. sin19π 24. sec 22π3

25. As viewed from above our solar system, a satellite orbits the earth once every 13 hours in thesame direction as the earth rotates. Assume that the satellite is above Greenwich, England att = 0.

a. Write a function θe(t) giving the angle the earth has rotated in t hours.

b. Write a function θs (t) giving the angle the satellite has rotated in t hours.

c. When will the satellite again be directly over Greenwich?

10-1E Practice Name ______________________________

Date _______________________________


Use nABC to find each length or angle measure.

1. a

2. m/A

3. m/B

C B

A

a

817

4. A string which runs from the top of a tent to a stake in the ground makes an angle of 508 with theground. If the string is 8 ft long, how high is the top of the tent?

5. Find the angle, in radians, formed by the minute and hour hands of a clock at 3:30.

6. A clock has a 5-cm second hand.

a. Give the angular speed of the hand in radians per minute.

b. Give the linear speed of a point at the end of the hand in meters per hour.

7. Cheyenne, Wyoming, latitude 41.18 N, is due north of Denver Colorado, latitude 39.88 N.

Find the distance between the two cities.

8. A pizza has radius 14 in. Give the area of a pizza slice with a central angle of 22.58.

9. A tricycle has a front wheel with diameter 18 in. A child is riding the tricycle at a speed of 4mi/hr. Find the angular speed of the wheel:

a. in revolutions per minute

b. in radians per minute

Give the value of each trigonometric ratio.

10. cos 3π4 11. tan 17π

6

12. csc(–4958) 13. cot 3158

Give the measure of the acute angle with each given value.

14. cos A = 0.1 15. sin B = 0.8

16. tan C = 0.7 17. sec D = 1.8

10-2A Practice Name ______________________________

Date _______________________________


Find each indicated side length for nABC. Where necessary, round answers to the nearest tenth.

1. m/A = 358, b = 14, c = 18. Find a.

2. a = 35, m/B = 628, c = 22. Find b.

3. a = 57, b = 42, m/C = 388. Find c.

4. m/A = 1258, b = 85, c = 60. Find a.

5. a = 7, m/B = 908, c = 24. Find b.

6. a = 23, b = 17, m/C = 1608. Find c.

7. m/A = 88, b = 32, c = 45. Find a.

A

BCa

b c

Find each indicated angle measure for nDEF. Where necessary, round answers to the nearest tenth ofa degree.

8. d = 15, e = 18, f = 23. Find m/E.

9. d = 32, e = 47, f = 25. Find m/F

10. d = 23, e = 35, f = 15. Find m/D.

11. d = 25, e = 25, f = 25. Find m/E.

12. d = 11, e = 8, f = 6. Find m/F.

13. d = 169, e = 120, f = 119. Find m/D.

14. d = 75, e = 93, f = 62. Find m/E.

FE

D

ef

d

15. The lengths of two sides of a parallelogram are 25 cm and 30 cm,and one angle of the parallelogram measures 508. Find the lengths ofthe diagonals of the parallelogram.

508

30 cm

25 cm

16. The speed of an airplane in still air is 350 mi/hr. There is a 50 mi/hr wind blowing due north.Find the actual speed of the airplane if it is directed:

a. to the south b. to the east

c. 308 west of north d. 508 east of north

17. Rhonda lives 25 miles north of downtown. Edward lives 35 miles southeast of downtown. Givethe distance between Rhonda’s home and Edward’s home.

18. Three circles are externally tangent, as shown. Their centers are A,B, and C, and their radii are 14, 22, and 12, respectively. Find themeasures of the three angles.

m/A

m/B

m/C

A

C

B

10-2B Practice Name ______________________________

Date _______________________________


Find each indicated side length for nPQR. Where necessary, round answers to the nearest tenth.

1. m/P = 388, m/Q = 248, p = 12. Find q.

2. m/Q = 858, m/R = 178, q = 11. Find r.

3. m/P = 1208, m/R = 108, r = 18. Find p.

4. m/P = 528, m/Q = 438, r = 25. Find q.

5. m/Q = 408, m/R = 1108, p = 34. Find r.

6. m/P = 158, m/R = 188, q = 8. Find p.

R

P

Q

r

p

q

Find each area. Round answers to the nearest tenth.

7. a = 23, b = 37, c = 42. Find the area of nABC.

8. j = 14, m/K = 438, l = 23. Find the area of nJKL.

9. x = 15, y = 23, z = 19. Find the area of nXYZ.

10. d = 20, m/E = 1208, f = 45. Find the area of nDEF.

11. r = 9, m/S = 438, t = 11. Find the area of nRST.

12. u = 62, v = 43, w = 57. Find the area of nUVW.

Find the missing measures for each nABC. Round answers to the nearest tenth.

m/A m/B m/C a b c Area nABC

13. 388 858 23

14. 258 728 14

15. 498 16 37

16. 1108 438 18

17. 34 18 29

18. 348 43 65

19. A parallelogram has side lengths 3.8 m and 5.9 m, and the measure of one of its angles is 388.

Find its area to the nearest hundredth.

20. From Ron’s home, the angle of elevation to the top of a tower is 488. From Jorge’s home, theangle of elevation is 328. Ron’s home is 50 m closer to the base of the tower than Jorge’s home.

Find the height of the tower.

10-2C Practice Name ______________________________

Date _______________________________


Find each indicated side length for nXYZ. Where necessary, round answers to the nearest tenth.

1. m/X = 478, m/Y = 738, x = 38. Find y.

2. x = 23, m/Y = 428, z = 38. Find y.

3. m/X = 258, m/Y = 1108, z = 50. Find x.

4. x = 28, y = 59, m/Z = 358. Find z.

5. x = 35, m/Y = 458, m/Z = 658. Find z.

6. m/X = 908, y = 48, z = 14. Find x.

Z

Y

X

z

y

x

Find each indicated angle for nUVW. Where necessary, round answers to the nearest tenth of adegree.

7. u = 13, v = 29, w = 27. Find m/U.

8. u = 62, v = 57, w = 43. Find m/V.

9. u = 38, v = 23, w = 50. Find m/W.

10. u = 27, v = 38, m/W = 708. Find m/U.

VU

W

vu

w

Find the missing measures for each nABC. Round answers to the nearest tenth.

m/A m/B m/C a b c Area nABC

11. 38 52 47

12. 418 12 17

13. 498 818 23

14. 758 528 35

15. A parallelogram has side lengths 18 in. and 26 in., and the measure of one of its angles is 1428.

a. Find the lengths of the diagonals.

b. Find the area of the parallelogram.

16. A surveyor finds that the sides of a triangular plot of land measure 360 ft, 395 ft, and 450 ft.

a. Find the measure of the largest angle of the triangle.

b. Find the area of the plot of land.

17. Cary and Terri are lifting a heavy object. Cary lifts with a force of 75 pounds, and Terri lifts witha force of 65 pounds. If the angle between the forces is 258, what is the magnitude of the resultantforce on the object?

10-3A Practice Name ______________________________

Date _______________________________


Give the amplitude and period of each periodic function.

1. amplitude

period

y5

x50

2. amplitude

period

y10

x2p0

Sketch the graph of each function, and give its amplitude and period.

3. y = cos 3x

amplitude

period

y5

x2p0

4. y = 3 sin 2x

amplitude

period

y5

x2p0

Give a sine function with each amplitude and period.

5. amplitude 4, period 2π 6. amplitude 3, period 5π

7. amplitude 1.7, period 3 8. amplitude 0.3, period 1

9. amplitude 2, period π4 10. amplitude 0.75, period 2π

5

10-3B Practice Name ______________________________

Date _______________________________


1. The graph at the right shows a cosine function.

a. What is the average y-value?

b. What is the amplitude?

c. What is the period?

y5

x2p0

Sketch the graph of each trigonometric function. Give the amplitude, period, average y-value, andphase shift of the function.

2. y = 2sin(3x − π)

amplitude

period

average y-value

phase shift

y5

x2p0

3. y = cos x − π2( ) − 3

amplitude

period

average y-value

phase shift

y5

x2p0

Give a sine function with the given values.

4. amplitude 1, period 2π , phase shift π2 , and average value 3

5. amplitude 3, period 3π, phase shift π , and average value 0

6. amplitude 5, period 1.5, phase shift 1, and average value –2

7. amplitude 0.25, period π2 , phase shift 0, and average value 1.8

8. amplitude 2.3, period 7, phase shift 3, and average value 3.7

9. amplitude 1.5, period 4π5 , phase shift π

5 , and average value –5.5

10-3C Practice Name ______________________________

Date _______________________________


Sketch the graph of each trigonometric function. Give the amplitude, period, average y-value, andphase shift of the function.

1. y = 32 sin x + π

2( ) + 12

amplitude

period

average y-value

phase shift

y5

x2p0

2. y = 2cos 2x3 − π

2( ) − 2

amplitude

period

average y-value

phase shift

y5

x2p0

3. Sketch a periodic function (not necessarily a sine or cosinefunction) with amplitude 3, period 2, and average y-value 1.

y5

x50

Give a sine function with the given values.

4. amplitude 4, period π3 , phase shift π

12 , and average value 10

5. amplitude 3, period π , phase shift π5 , and average value –2

6. amplitude 2.5, period 5, phase shift 3, and average value 0

7. amplitude 1, period 3π, phase shift π , and average value 4

8. amplitude 1.7, period 1, phase shift 0, and average value 2.5

9. amplitude 0.6, period 2π , phase shift π4 , and average value 1

11-1A Practice Name ______________________________

Date _______________________________


A spinner for a game has nine congruent sectors numbered 1 through 9. Find each probability for asingle spin of the spinner.

1. that you spin a 5

2. that you spin a 6 or a 7

3. that you do not spin a 6 or a 7

4. that you spin an even number or a 5

5. that you spin an odd number or a number greater than 6

Refer to the table of Scrabble tiles on page 757 of your textbook to help find each probability. Expressanswers as decimals.

6. that the first tile drawn is an M

7. that the first tile drawn is worth at least 8 points

8. that the first tile drawn is a vowel or is worth 2 points

9. that the first tile drawn is worth 2 or 4 points

10. that the first tile drawn is a W, X, Y, or Z

11. In a class of 25 students, there are 15 freshmen. There are 10 boys, and the probability that afreshman is a boy is 0.4. What is the probability that a student chosen at random from the class isa freshman or is a boy?

Refer to the illustration of a set of dominoes on page 761 of your textbook. Find each probability,expressing your answer as a decimal rounded to the nearest thousandth.

12. that a randomly chosen domino has a 4 on at least one side

13. that a randomly chosen domino does not have a 4 on at least one side

14. that a randomly chosen domino has an odd number on at least one side

15. that a randomly chosen domino is not the same on both sides of the bar

16. that a randomly chosen domino has a 5 or a 6 on at least one side

17. A used car lot has 100 cars. 15 of the cars are red, and 25 of the cars are hatchbacks. If there are 5red hatchbacks, find the probability that a car chosen at random is red or is a hatchback.

18. Stu and Sue are members of the Drama Club, which has 20 members. The club is choosing acommittee of 5 members to discuss the club’s budget.

a. How many different ways can 5 of the Drama Club members be selected?

b. If Sue and Stu are chosen, how many ways can the remaining three committee members be selected from the remaining 18 club members?

c. What is the probability that Sue and Stu are both chosen to be on the committee, if the committee is chosen at random?

d. What is the probability that Sue and Stu are not both chosen?

11-1B Practice Name ______________________________

Date _______________________________


Decide whether the two events are dependent or independent and explain why.

1. getting an A in mathematics and getting accepted to your favorite college

2. getting into a traffic accident on the way to an appointment and being on time for thatappointment.

3. drawing the king of spades from a deck of cards and flipping a coin that lands on heads

Let A, B, and C be independent events and P(A) = 0.18, P(B) = 0.31, and P(C) = 0.65. Find eachprobability.

4. P(A and B) 5. P(B and C)

6. P(A and C) 7. P(A and B and C)

8. Ralph estimates that he has a 60% chance of getting an A on his English test, and a 45% chanceof getting an A on his physics test. What is the probability that he gets an A on both tests,assuming that the events are independent?

9. Suppose that you randomly choose a pen and a pad of paper from your drawer to take to thelibrary. If five of your twenty pens are black and three of your five pads of paper are illustrated,what is the probability that you choose a black pen and an illustrated pad?

10. A game requires you to toss three dice each turn.

a. What is the probability that you will roll three sixes during a turn?

b. What is the probability that you will roll three of a kind during a turn?

c. If you play the game for five turns, what is the probability that you will not get three of a kindduring any turn?

11. Suppose a machine consists of two components, component A and component B, and themachine can function properly only if its components are functioning properly. On any givenday, component A has a 5% probability of failure and component B has a 10% probability offailure. Assume that the component failures are independent events.

a. Find the probability that component A will not fail on a given day.

b. Find the probability that component B will not fail on a given day.

c. On any given day, find the probability that the machine will work correctly all day.

d. What is the machine’s probability of failure on a given day?

11-1C Practice Name ______________________________

Date _______________________________


Decide whether the two events given (a) are dependent or independent, and (b) involve sampling withreplacement, sampling without replacement, or neither.

1. choosing a marble from a bag and giving it to a friend, then choosing another marble

a. b.

2. choosing a card from a deck, and then rolling a die without replacing the card

a. b.

3. choosing a winning raffle ticket from a bin, replacing it, and then choosing the winning ticket foranother prize

a. b.

Recall that there are 100 scrabble tiles, including 9 A’s, 2 H’s, 1 Q, and 4 U’s. Find each probabilityfor the first two tiles drawn without replacement.

4. P(H)A) 5. P(U)U)

6. P(H)H) 7. P(Q)Q)

8. P(A)H) 9. P(Q)A)

Two cards are drawn from a deck of 52 playing cards without replacement. Find each probability.

10. P(red card)red card) 11. P(4)Q)

12. P(3)3) 13. P(club)diamond)

14. P(heart)heart) 15. P(4)spade)

16. Suppose the probability that a person has a particular disease is 0.5%. If a person has the disease,a medical test gives a positive result 95% of the time. If a person does not have the disease, thetest gives a false-positive result 0.1% of the time.

What is the probability that a person with a positive test actually has the disease?

17. At Johnson High School, 35% of the freshmen are enrolled in a biology class. Of the freshmenwho are in a biology class, 10% are in the marching band. Find the probability that a freshmanchosen at random is in a biology class and in the marching band?

18. Find the probability that a card chosen at random from a 52-card deck of playing cards is:

a. a diamond, given that it is a red card

b. a 3, given that it is not an even-numbered card

c. a club, given that it is a queen

11-1D Practice Name ______________________________

Date _______________________________


Decide whether the two events are dependent or independent and explain why.

1. tossing a coin and then choosing a Scrabble tile

2. having sunny weather today and having sunny weather tomorrow

3. winning the lottery and having money

The table shows the distribution of the Scrabble tiles in the first part of the alphabet.Find each probability. If necessary, round answers to the nearest hundredth.(Note: The total number of tiles is 100.)

Tile Number Points

A 9 1

B 2 3

C 2 3

D 4 2

E 12 1

4. that the first tile drawn is an E

5. that the first tile drawn is a C or a D

6. that the first tile drawn is not an A, B, C, or D

7. that the first tile drawn is worth 3 points, given that it is an A, B, C, D, or E

8. that the first two tiles drawn are E’s if the first tile is replaced before drawing the second

9. that the first two tiles drawn are E’s if the first tile is not replaced before drawing the second

10. Atsushi’s coin collection includes 25 nickels and 10 coins dated 1952. There are three 1952nickels. If there are 200 coins in the collection, what is the probability that a coin chosen atrandom is dated 1952 or is a nickel?

11. Estelle has determined that, when she goes to the library, there is a 40% chance that the librarywill have one or more books by her favorite author on the shelf. When one or more books areavailable, there is a 70% chance that she has already read all of them. Estelle is going to thelibrary today. What is the probability that she will find a book that she has not read by herfavorite author

11-2A Practice Name ______________________________

Date _______________________________


Identify the population being studied in each situation. Would you study the entire population or asample? Why?

1. A candy manufacturer wants to know if children like the taste of their new recipe.

2. A publisher wants to make sure that its books have no typographical errors.

3. A teacher wants to test students to make sure they understand the lesson and to assign grades.

4. Sketch a histogram for the data set 1, 3, 7, 2, 5, 6, 3, 8, 9, 4, 3, 2,

6, 8, 4, 2, 6, 8, 5, 2. Use percentages along the vertical axis.

5. A researcher finds that 8 out of 100 people in a small town have been exposed to a particular

virus. If there are 6000 people in the town, what will be the estimate of the number people in the

town who have been infected?

In each situation, explain why the sample obtained may be biased.

6. Vong surveys his calculus class in order to determine what percentage of the students at his

school like football.

7. A political organization conducts a survey of public opinion by sending questionnaires to people

on its mailing list.

8. A restaurant reviewer introduces herself to the chef before her meal at a restaurant she is

reviewing.

11-2B Practice Name ______________________________

Date _______________________________


Suppose that a data set is normally distributed with a mean of 75 and a standard deviation of 5.Complete each statement.

1. Approximately 68% of the data values lie between and .


3. Approximately 2.3% of the data values are less than .

4. Approximately 2.3% of the data values are greater than .

Suppose that a data set is normally distributed with a mean of 1000 and a standard deviation of 25.Complete each statement.

5. Approximately of the data values are between 1000 and 1025.



8. Approximately of the data values are greater than 1050.

State whether you believe that a normal distribution would be a good model for each data set. Explainyour answers.

9. the heights of American men

10. the useful lifetimes of refrigerators

11. the number of hours that employed Americans work during an average week

12. the face values of individual coins produced by the U.S. Mint

13. A machine produces candy bars which have a mean weight of 2.1 oz, with a standard deviation of0.1 oz. When the machine is operating normally, what percentage of candy bars will weigh lessthan 2 oz?

Explain.

14. A tire manufacturer offers a 6-year warranty. Research has shown that their tires last an averageof 9 years, with a standard deviation of 1.5 years.

a. Estimate the probability that a tire will fail during the warranty period.

b. Estimate the probability that a tire will last at least 10.5 years.

c. Estimate the probability that a tire will last at least 9 years.

d. Estimate the probability that a tire will have a lifetime between 6 and 7.5 years.

11-2C Practice Name ______________________________

Date _______________________________


Identify the population being sampled in each situation. Would you study the entire population or asample? Why?

1. A photographic film manufacturer wants to ensure that the film it produces meets specifications.

2. A researcher wants to estimate the average amount of water that an American drinks each day.

3. Sketch a histogram for the data set

2, 6, 18, 20, 14, 16, 18, 4, 6, 14, 18, 16, 18, 12, 16, 20, 14, 12,16, 8, 6, 16, 14, 18, 8.

Use percentages along the vertical axis.

4. A study of the American educational system is conducted by interviewing teachers in affluentcommunities. Explain why the sample obtained may be biased.

5. A survey shows that 80 out of 140 voters plan to vote for Jones. If a representative sample hasbeen chosen and there are 2,000,000 voters, how many of them can be expected to vote forJones?

Suppose that a data set is normally distributed with a mean of 63 and standard deviation of 8.Complete each statement.



8. Approximately 2.3% of the data values are less than .

9. Approximately 2.3% of the data values are greater than .

10. The average Martian is 48 cm tall with a standard deviation of 7 cm. The heights of Martians arenormally distributed.

a. Find the probability that a Martian is between 41 and 55 cm tall.

b. Find the probability that a Martian is between 55 and 62 cm tall.

c. Find the probability that a Martian is between 34 and 48 cm tall.

d. Find the probability that a Martian is less than 34 cm tall.

12-1A Practice Name ______________________________

Date _______________________________


Verify Euler’s Formula for each polyhedron.

1.

2.

3. A simple polyhedron has 6 faces and 8 vertices. How many edges does it have?

4. A simple polyhedron has 15 edges and 10 vertices. How many faces does it have?

5. Analyze this graph representing a dodecahedron.

a. How many vertices does the graph have?

b. How many edges does the graph have?

c. The graph divides the plane into how many regions?

6. Abe, Brad, Connie, Duffy, Elmer, and Farshid met recentlyfor dinner. Connie shook hands with everybody, and Duffyshook hands with everyone except Abe. In addition, Bradshook hands with Elmer and Abe shook hands with Farshid.Draw a graph representing the handshakes that took place.

7. This graph shows six cities and the telephone connectionsbetween the cities.

a. How many telephone connections are there?

b. How many telephone connections would need to be addedso that there would be a direct line between each pair of cities?

G H I

J K L

8. Suppose that there are four houses in a row, and across thestreet there are two utility connections. Is it possible to makeseparate connections from each house to each utility withoutany connections crossing?

Explain or illustrate.

12-1B Practice Name ______________________________

Date _______________________________


Decide whether each graph is connected.

1. 2.

Explain why each path is or is not an Euler path.

3.

3

2 7

4 5

61

4.

8

1 5

7 3

426

Give the degrees of the vertices in each graph. Determine whether the graph has an Euler circuit orpath and identify one if so.

5. A B C

D E F

G H I

J K L

A B

CD

E IF

HLJ

G

K

6. A B C

D E F

A

B C

D

E F

7. Add one or more edges to the graph at the right so that the newgraph has an Euler circuit. Identify the Euler circuit.

A B

CD

E F

8. Is is possible for a graph to have exactly one vertex with an odd degree?

Explain.

12-1C Practice Name ______________________________

Date _______________________________


Give a Hamiltonian circuit for each graph.

1.

A B

C

DE

F G H

2.

A B C

DEF

GH I

Decide whether the graph is a tree. Explain your reasoning.

3.

4.

Give a minimal spanning tree for each graph.

5.

A B C D

EF

G

H I

3 4 5

1116

5 9 7 17

15 613

12

10 14

6.

A B

DE

FG

H

4

2

1132

33

7

17

30

21

2824 C

7.

7

4

6020

42

13

30

1017

15 12

55

25

G

EF

CB

A D

8.

GHE

F

CBA D

KJI L

6

9

1

13

16

8

3

7 5 4

17

14 10 15 12

2 11

9. Draw a graph representing the figure shownand give a Hamiltonian circuit for the graph.

10. A traveling sales representative needs to visit each of the fourcities shown, beginning and ending in A. The graph shows thenumber of driving miles between each pair of cities. How shouldthe sales representative plan the trip in order to minimize thenumber of miles driven?

A B

CD

90 mi 88 mi

45 mi

36 mi

100 mi75 mi

12-1D Practice Name ______________________________

Date _______________________________


1. The following pairs of people exchanged giftsduring the holiday season:

Frederick and Gerald; Frederick and Harold;Frederick and Ingrid; Frederick and Kate; Geraldand Harold; Gerald and Ingrid; Harold and Ingrid;Harold and Josephine; Harold and Liz; Josephineand Liz; Kate and Liz

Draw a graph representing the gift exchanges.

2. Give an Euler circuit and a Hamiltonian circuit forthe graph at the right.

Euler

Hamiltonian

B DC

A

H I

G F E

3. The graph shows the cost, in hundreds of dollars,of installing intercom connections between offices.Any connections not shown are too expensive.Find a minimal spanning tree and give theminimum cost of installing the intercom system.

T W

U V

Y X

Z

7 3

344

4

5

75 10

6

8

8

6

4. A simple polyhedron has 10 vertices and 9 faces. How many edges does it have?

Determine whether each graph has an Euler circuit, an Euler path, or neither. Explain.

5.

G C

H B

F D

A

E

6.

J

I K

OL N

M

Decide whether each graph is a tree. Explain your reasoning.

7.

8.

12-2A Practice Name ______________________________

Date _______________________________


Give the first eight terms of each sequence and sketch the graph of the sequence.

1. a1 = 100 and an + 1 = 0.5an + 10

2. a1 = 2 and an = –1.5an – 1 + 1

Give an explicit formula of the form an = h + kAn for each recursively defined sequence. Use yourformula to find the tenth term and to determine if the sequence converges.

3. an = 2an−1 + 3; a1 = 6 a10 =

4. an = 13 an−1 + 3; a1 = 81 a10 =

5. an = −an−1 + 3; a1 = 3 a10 =

6. an = −2an−1 − 4; a1 = 10 a10 =

7. an = 10an−1 + 5; a1 = 1 a10 =

8. an = −0.5an−1 + 10; a1 = 20 a10 =

9. Lawrence opened a bank account with $600 at the beginning of the year. The account pays 8%interest at the end of each year, and Lawrence plans to deposit $400 in the account at thebeginning of each year. Define a recursive sequence that gives the amount in the account at thebeginning of each year.

In how many years will Lawrence’s account balance exceed $20,000?

10. Lucinda is very successful at buying stocks which she can sell at a price that is 10% higher thanthe purchase price. Her broker charges a $200 commission every time she sells. If she starts with$10,000, write an explicit formula of the form an = h + kAn . For the amount she has after she hasbought and sold n – 1 stocks, and determine whether the sequence converges.

How would your answer change if she started with $2000?

12-2B Practice Name ______________________________

Date _______________________________


Decide whether each matrix is a transition matrix. Explain your reasoning.

1.12

12

23

13

2.

0.7 1.1

0.3 −0.1

3.63 82

37 18

4.

0.3 0.5

0.6 0.2

0.1 0.3

Give the missing transition probabilities in each transition matrix.

5.

0.5 0.2

6. 0.91

0.23

7.0.3 0.7

8.0.128

0.895

Calculate several powers of each transition matrix and give the limit matrix to which these powersconverge.

9. A =0.3 0.4

0.7 0.6

A2 A3 L

10. B =0.2 0.8

0.8 0.2

B2 B3 L

11. C =0.85 0.35

0.15 0.65

C2 C3 L

12. D =0.56 0.83

0.44 0.17

D2 D3 L

13. At Montgomery High School, 75% of the students who wear jeans one day will be wearing jeansthe next day. Of the students who do not wear jeans on any particular day, 45% will be wearingjeans the next day. There are 1000 students, and none of them wore jeans the first day of school.

a. Write a transition matrix for this situation.

b. Predict the number of students who wore jeans on the second day, the third day, the fourth day, and in the long run.

second third fourth long run

12-2C Practice Name ______________________________

Date _______________________________


Give the first eight terms of each sequence and sketch a graph of the sequence.

1. a1 = 5 and an = 2an−1 − 4

2. a1 = 10 and an+1 = 0.5an − 2

Give an explicit formula of the form an = h + kAn for each recursively defined sequence.Use your formula to find the tenth term and determine if the sequence converges.

3. an = 3an−1 + 20; a1 = 4 a10 =

4. an = 0.2an−1 + 1; a1 = 100 a10 =

5. an = −0.5an−1 + 25; a1 = 1000 a10 =

Calculate several powers of each transition matrix and give the limit matrix to which these powersconverge.

6. A =0.1 0.3

0.9 0.7

A2 A3 L

7. B =0.8 0.4

0.2 0.6

B2 B3 L

8. Ron had $5000 at the beginning of the year. Every week, he has spent 15% of his savings andthen cashed his $600 paycheck, which is added to his savings. How much does Ron have at thebeginning of the

second week? the third week?

the nth week

9. A long-distance telephone company finds that every month, 10% of its customers switch toanother company and 15% of people who are not customers become customers. There are1,000,000 people in the area that the company serves.

a. Write a transition matrix for this situation.

b. If 500,000 people are customers this month, how many do you predict will be customers next month? the month after that? in the long run?

Answers


CHAPTER 1

1-1 Part A

1. Positive association 2. No association 3. Positiveassociation, because the area of a square increases whenthe perimeter increases. 4. No association, because thequantities are not related. 5. Negative association,because cooler temperatures mean more energy used forheating. 6. Negative association, because oldercomputers are often obsolete.7. a.

1986 1989 1992

20

30

10

40

Year

Cri

mes

b. Positive associationc. About 40d. About 28; About 30

1-1 Part B1. 3; 4.5; y = 1.5x – 3

y5

x5

2. –4; –6; y = –2x + 4y5

x5

3. a. m = 32g b. g; m c. 224 mi 4. a. p = 7.5hb. $150 c. p = 8.25h d. $155. Possible answer:

x 0 1 2 3 4 5

y –2 1 4 7 10 13

6. Possible answer:

x 0 1 2 3 4 5

y 5 3 1 –1 –3 –5

7. Possible answer:

x 0 1 2 3 4 5

y 3 2 –1 –6 –13 –22

8. Possible answer:x 0 1 2 3 4 5

y 1 112

2 212

3 312

1-1 Part C

1. Not a function 2. Function; D = {–1, 0, 1, 2};R = {2, 3, 4} 3. Function; D is the set of real numbers;R is the set of nonnegative real numbers. 4. Function; Dis the set of names of students in the class; Possibleanswer: R = {A, B, C, D, F} 5. Function; D is the set ofreal numbers; R is the set of real numbers that are greaterthan or equal to –1. 6. Not a function 7. a. –$5.00b. $88.75 c. $95.00 d. $92.75

e. Possible answer: The store is losing money by sellingthe soup at this price. f. $1.50; This price produces themaximum profit. 8. a. 10 b. –5 c. –2 d. 319. a. 2 b. 0 c. 2 d. 4

1-1 Part D

1. Negative association; A trip taken at a faster speed willtake less time. 2. No association; The day of the monthdoes not normally affect newspaper sales.3. 0; –0.5; y = –1

2x + 2

y5

x5

4. Not a function5. Not a function6. Function; The domain isthe set of real numbersgreater than or equal to 9.The range is the set ofnonnegative real numbers.

7. a. 8 miles b. d = 32t c. t ; d d. 7 hours

1-2 Part A

1. {heads/heads, heads/tails, tails/heads, and tails/tails}

2. AC, AD, BD, { BE, CE} 3. {Monday, Tuesday,

Wednesday, Thursday, Friday, Saturday, Sunday} 4. 52

5. 30 6. 6 7. 2 8. 4 9. 4 10. a. 113

b. 14

c. 152

d. 513

11. a. 19 b. 4

9 c.

10 27 d.

2227

12. a. 18

b. 1160

c. 37120

d. 83120

1-2 Part B

1. Possible answer: Use a random number table and let thedigits 1–7 represent nearsighted students. 2. Possibleanswer: Roll a die and let the numbers 1–4 representpeople who watched the meeting. 3. Possible answer:Flip a coin and let “heads” represent relatives who enjoybowling. 4. a. 1

2 b. No; Possible answer: A storm

may last for several days, so snow is more likely to fall onconsecutive days than it would be if snowfall wererandom. 5. Possible answer: Let 1 represent a lostgame, and consider groups of three digits.6. Possible answers: a. 4

5 b.

15 c. 0 7. No; Possible

answer: His competition is probably much stiffer thanusual. 8. Possible answer: Let heads/heads represent acorrect answer. 9. Check students’ answers.10. Check students’ answers. Answers should add to 1.

Theoretical probabilities are a. 164

, b. 9

64, c. 27 64, and d.

27 64.

1-2 Part C

1. 6 2. 5 3. 2 4. 115 5. a.

14

b. 17 c. 3

7 d. 1

28 e.

12 f.

27 6. 5

64 7. Possible

answer: 37; Let the digits 1, 2, 3, and 4 represent students

from Barbara’s intermediate school. Since 9 out of 21groups of three digits contain exactly two of these digits,

the approximate probability is 9 21

= 37

. 8. 45

Answers


1-3 Part A

1.

1 3

12 0

1 8

2.

1 2 −3 −5

−2 8 −1 1

3.

−4 8

14 −6

6 8

4.

−7 9

9 −9

8 4

5. −1 1 −3 −2

−4 3 2 0

6. 4 5 −6 −13

−2 21 −5 3

7. 2 3 48.

y5

x5

a.

b.

a. −5 −2 −1

1 4 0

; Triangle is

translated by <–3, 2>

b. −4 2 4

−2 4 −4

; Triangle is

dilated by a factor of 2

9. a.

2 30 −9

42 −20 21

5 −11 33

b.

88 76 99

88 66 87

61 101 97

c. Strawberry ice cream in regular cone

d.

176 152 198

176 132 174

122 202 194

1-3 Part B

1. 0; –2; 1; 1; −6 −5

3 3

2. –2; 3; –2; 4; 1; 1; –2; 1; 2;

0 8

16 0

−11 −1

3. No

4. Yes; 5 3 3 5. 4 4 5

11 6 −6

6.

−13 8 19

−26 10 27

10 −2 −7

7.

1 21

3 2

−3 32

8. Not possible because S has 2 columns

but U has 3 rows. 9. 1 13

2 −11

10. Not possible

because U has 3 columns but T has 2 rows. 11. No

12. No 13. Yes 14. a.

45 34 54

63 24 64

35 34 65

24 75 25

;

$5.99

$7.99

$9.99

b.

$1080.67

$1208.49

$1130.66

$992.76

c. The entries in the matrix product

show the total sales for these products in July, August,September, and October, respectively.

1-3 Part C

1. –2 2.

1 2 −4

3 7 −2

−4 3 −1

×1 0 0

0 1 0

0 0 1

=1 2 −4

3 7 −2

−4 3 −1

3.

0 9 −5

2 5 2

7 5 3

4. Not possible because the matrices do not have the same

dimensions. 5. 6 12 −3

12 −12 9

6.

4 −1 −1

−4 −7 6

−1 −1 7

7.

−12 12 −2

14 26 −16

10 8 −18

8. 4 31 −10

−8 5 −6

9.

32 −28

28 −22

8 −8

10. Not possible because G has 2

columns but H has 3 rows. 11. HF =

−4 25 −6

15 1 −4

20 42 −20

12.

2 −20 11

−3 41 −22

7 −6 0

13. a.

15 20 10 8 12

14 21 30 5 10

16 18 15 7 11

18 25 30 10 15

;

6.50

8.50

9.00

5.00

7.50

b.

487.5

639.5

509.5

762.0

CHAPTER 2

2-1 Part A

1. 12

2. –2 3. 23

4. –52 5.

23 6.

2617 7. Linear;

m = 25; Direct variation 8. Not linear 9. Linear;

m = 4; Not direct variation 10. Linear; m = 23; Direct

variation 11. Linear; m = 2; Not direct variation12. Not linear 13. Linear; m = 2; Direct variation14. Not linear 15. P(x) = 2x + 20; Yes; No


y50

x20

16. 35

2-1 Part B

1. x = –4 2. x = 13 3. x = 3 4. k = –21 5. y = 106. No solution 7. a = –2 8. a = 3 9. z = 710. All real numbers 11. p =

12 12. k = –1

13. x = 9 14. y = 10 15. j = 2 16. t = 25 17. (b)and (c) 18. (a), (c) and (d) 19. a. c = 0.25 + 0.15ab. 4 = 0.25 + 0.15a; a = 25 c. 26 minutes20. a. a = 0.015v b. 30,000 = 0.015vc. v = 2,000,000

2-1 Part C

1. y = 3x + 3 2. y = 12x – 1

2 3. y = –3

2x + 3 4. y = 5

3x

5. y = –12x + 22 6. y = 2x + 8 7. y = 5

2x – 2

8. y = –2.17x + 5 9. y = –52x + 2 10. y = 1

2x + 4

11. y = –4 12. x = –3 13. y = –23x + 1

14. y = 2x – 3 15. a. d = –50t + 335

b. 335 mi c. 50 mi/hr d. At t = 6.7 hours

2-1 Part D1. Linear; Direct variation; m = 4 2. Not linear3. Linear; Not direct variation; m = –2 4. Linear;

Not direct variation; m = –23

5. 10; Shelley has been

gaining 10 clients per month. 6. –2 7. 48. –2; 2 9. 2

3; –3

y5

x5

y5

x5

10. x = 7 11. p = 5 12. k = 2 13. y = –4

14. 20 hours 15. y = 2x – 1 16. y = 13x -

113

17. y = 3x + 10 18. y = 12x + 4

2-2 Part A

1. y = –23x + 7; 3 2. y = 1

2x + 3; 5

3. Possible answer:y = –x + 9.75

y10

x10

4. Possible answer:

y = x + 12

y10

x10

5. a.s

20

k10

b. Possible answer:

y = 2 + 53x

c. About 12 sales

2-2 Part B1. 9, 9, 9 2. 7, 8, 7 3. 12, 11, 12 4. (5, 6)

5. 8 23 , 8( )

6.y

10

x10

a. (2, 3), (3, 3); (4, 5), (5, 5),(5, 6); (6, 6), (7, 8)

b. 2 12 , 3( ), 14

3 , 163( ),

6 12 , 7( )

c. 4 23 , 5( ) d. 1

e. y = x + 13

2-2 Part C1. Possible answer: Number of people in a party and thedollar amount of the food they purchase; Predict the dollaramount of the food a group of customers will purchase.2. Possible answer: Number of students involved in aproduction and the number of people who attend theproduction; Predict the number of people who attend aproduction. 3. Possible answer: Number of studentsenrolled and the number of bandages used in a year;Predict the number of bandages needed for a year.

4. a. y = –0.795x + 9.410;y = –0.881x + 9.947b.

y10

x10

c. 3.05, 2.899

5. a. y = 6.733x + 65.967b.

y100

x5

c. 77.75

d. No; Possible answer: The line would predict a score ofabout 120, but the total possible is probably only 100.

Answers


2-2 Part D

1. y = –32x + 40 2. Negative association

3. Both are negative. 4. 13 5. (4, 10)6.

y10

x10

a. 3, 5 12( ), 6, 5( ), 8 1

2 , 3 12( )

b. 5 56 , 4 2

3( ) c. − 411

d. y = – 411

x + 62633

7. a. y = 0.4874x + 2.530b. c. 5.94

0

y10

x10

2-3 Part A

1. t ≤ 2 2124 23 22 0 1 2 3 4

2. k ≤ −1 2124 23 22 0 1 2 3 4

3. s < 23

2124 23 22 0 1 2 3 4

4. x > –2 2124 23 22 0 1 2 3 4

5. p ≥ −1 2124 23 22 0 1 2 3 4

6. y > 1 2124 23 22 0 1 2 3 4

7. Possible answer: x ≤ 3 8. Possible answer: x > –39. 5 or more hours10. x ≤ 0 or x ≥ 2

2124 23 22 0 1 2 3 4

11. –3 < x < 0 2124 23 22 0 1 2 3 4

12. a < 1 or a > 3 2124 23 22 0 1 2 3 4

13. k ≤ −3 or k ≥ 2 2124 23 22 0 1 2 3 4

14. −1 ≤ p ≤ 4 2124 23 22 0 1 2 3 4

15. 1 < x ≤ 3 2124 23 22 0 1 2 3 4

16. y ≤ −1 or y > 4 2124 23 22 0 1 2 3 4

17. Possible answer: −2 ≤ x ≤ 1 18. Possible answer:x < –3 or x > –1 19. No more than 13 cans

2-3 Part B1. 3 2. 25 3. 0.34. x = 0 or x = 1

2124 23 22 0 1 2 3 4

5. x = 0 or x = 1 2124 23 22 0 1 2 3 4

6. x = –23 or x = 2

3

2124 23 22 0 1 2 3 47. x = 1 or x = 3

2124 23 22 0 1 2 3 48. x = –3 or x = –1

2124 23 22 0 1 2 3 49. x = –1 or x = 1

2124 23 22 0 1 2 3 410. (b)11. 2 ≤ y ≤ 4

2124 23 22 0 1 2 3 4

12. p ≤ − 72 or p ≥ − 1

2 2124 23 22 0 1 2 3 4

13. –3 < a < 1 2124 23 22 0 1 2 3 4

14. t < 23 or t > 4

3 2124 23 22 0 1 2 3 4

15. j ≤ − 32 or j ≥ 5

2 2124 23 22 0 1 2 3 4

16. –2 < x < 4 2124 23 22 0 1 2 3 4

17. Possible answer: x − 2 = 1

18. Possible answer: x +1 > 2 19. Possible answer:

x + 2 = 2 20. Possible answer: x −1 ≤ 1

2-3 Part C

1. y < x + 2 2. y ≥ 32 x −1

3. 4.y

5

x5

y5

x5

5. 6.y

5

x5

y5

x5

7. 600x + 300y ≥ 1000

2-3 Part D

1. x > 2 2124 23 22 0 1 2 3 4

2. x ≤ −1 2124 23 22 0 1 2 3 4

3. x ≤ −2 or x ≥ 1 2124 23 22 0 1 2 3 4

4. –1 < t < 3 2124 23 22 0 1 2 3 4


5. y < –3 or y ≥ −1 2124 23 22 0 1 2 3 4

6. 0 < c ≤ 32

2124 23 22 0 1 2 3 4

7. x = –85 or x = 8

5

2124 23 22 0 1 2 3 48. x = 1 or x = 3

2124 23 22 0 1 2 3 4

9. x = –32 or x = –

12

2124 23 22 0 1 2 3 4

10. x ≤ − 12 or x ≥ 5

2 2124 23 22 0 1 2 3 4

11. –4 < x < 0 2124 23 22 0 1 2 3 4

12. No solution 2124 23 22 0 1 2 3 4

13. Possible answer: h − 8 ≤ 14

14. Possible answer: 35a +15b ≤ 20015. 16.

y5

x5

y5

x5

CHAPTER 3

3-1 Part A1. (1, 3)

y5

x5

2. (4, 3)y

5

x5

3. (–3, 3)y

5

x5

4. 12 , 2( )

y5

x5

5. (–2, 2)y

5

x5

6. (1, –1)y

5

x5

7. a. 5 pounds b. United Shipping

3-1 Part B

1. (1, 4); 1 solution; consistent 2. (3, 3); 1 solution;consistent 3. No solution; inconsistent 4. (2, –1); 1solution; consistent 5. (1, –1); 1 solution; consistent6. (8, 4); 1 solution; consistent 7. (–1, 3); 1 solution;consistent 8. (7, 5); 1 solution; consistent 9. (2, –3);1 solution; consistent 10. Any ordered pair (x, y)satisfying 2x + 7y = 10; Infinitely many solutions;consistent 11. a. x + y = 600 and 0.2x + 0.35y =0.25(600), or equivalent b. (400, 200); The chemistshould use 400 ml of 20% solution and 200 ml of 35%solution. 12. 2 lb broccoli and 5 lb carrots13. a. Chain Gang: y = 12 + 2x; Wacky Wheels: y = 5 + 3xb. 7 days

3-1 Part C

1. 1 2

1 −2

x

y

=6

12

2.

2 −1

5 −3

x

y

=−1

−1

3. 1 2

−2 1

x

y

=1

−7

4. 2 3

−3 −5

x

y

=−2

2

5. 1 −1

4 −5

x

y

=1

1

6. 3 −8

2 −5

x

y

=−9

−5

7. 9, − 32( ) 8. (–2, –3) 9. (3, –1) 10. (–4, 2)

11. (4, 3) 12. (5, 3) 13. 9 3

4 2

x

y

=4.50

2.30

14. 1 1

48 60

x

y

=6

318

15. Super X: 35¢; Mighty Y:

45¢ 16. x = 312; y = 21

2

3-1 Part D

1. x = 2, y = 3, z = –2 2. x = 3, y = –4, z = 1 3. x = 83,

y = – 23, z = –1 4. x = 4, y = –2, z = 3 5. x = 1, y = 3,

z = 4 6. x = 5, y = 2, z = 4 7. 248, 278, and 12988. Dates: $1.50/lb; Endives: $0.85/lb; Figs: $2.35/lb

9.

2 4 3

4 −2 1

−1 3 4

x

y

z

=6

4

−2

; x = 19

10 , y = 1310 , z = −1

10.5 −2 3

−2 4 6

8 7 −3

x

y

z

=4

3

−6

; x = 9

164 , y = − 89164 , z = 433

492

(or x < 0.055, y < –0.543, z < 0.880)

11.

2 −3 1

−5 2 338

74

34

x

y

z

=4

−3

6

; x = 744

253 , y = 399253 , z = 721

253

(or x < 2.941, y < 1.577, z < 2.850)

Answers


12.

3.5 2.2 −2.7

4.3 −1.8 2.3

3.6 1.3 5.3

x

y

z

=4.3

2.5

2.9

; x < 0.842, y < 0.450,

z < –0.135

3-1 Part E1. (b) 2. (a) 3. (–2, 5); 1 solution; consistent4. (3, –5); 1 solution; consistent 5. (3, 2); 1 solution;consistent 6. All ordered pairs that satisfy 2x + 3y = 5;Infinitely many solutions; consistent 7. (–4, –5); 1solution; consistent 8. No solution; inconsistent9. 9 gal regular and 6 gal premium

10. 3 −2

−7 5

x

y

=−4

3

; x = −14, y = −19

11.

2 −5 −3

1 −3 −1

−2 6 3

x

y

z

=2

5

−2

; x = 13, y = 0, z = 8

12. Asparagus: $2.00; Broccoli: $1.00; Cabbage: $0.50

3-2 Part A

1. y5

x5

2. y5

x5

3. Possible answer: Let x be the amount that Mariaspends; x ≤ 300 4. Possible answer: Let n be thenumber of notebooks that Jose buys; n ≥ 55. y

5

x5

6. y5

x5

7. a. x + y ≤ 2000; x ≤ 23 y b. x ≥ 0; y ≥ 0

c. y2000

x20000

3-2 Part B

1. (–3, –3), (3, –1), (0, 3)y

5

x5

2. (–3, –2), (–3, 2), (1, 4),(4, –2)

y5

x5

3. (0, 0), (0, 7), (7, 3),(8, 0)

10

10

y

x

4. (0, 0), (0, 40), (40, 30),(20, 0)

50

50

y

x

5. x ≥ 0, y ≥ 0,x + y ≤ 25, x ≤ 15;(0, 0), (0, 25), (15, 10),(15, 0)

25

25

y

x

6. Possible answer:r ≥ 0, t ≥ 0, 15r + 25t ≤ 175, r ≤ 5;(0, 0), (0, 7), (5, 4), (5, 0)

10

10

t

r

3-2 Part C

1. Possible answer: P = 5b + 20p 2. Possible answer:C = 90b + 60v 3. Possible answer: N = x + y4. a. x ≥ 5, y ≥ 0, y ≤ 15, x + y ≤ 25b. (5, 0), (5, 15), (10, 15),(25, 0) c. I = 5x + 7yd. (10, 15); He shouldwork 10 hours for X and15 hours for Y. e. $155

25

25

y

x

5. a. x ≥ 0, y ≥ 0, 0.4x + 0.3y ≤ 18; 0.1x + 0.35y ≤ 10b. (0, 0), 0, 28 4

7( ) ,(30, 20), (45, 0)c. F = x + y d. (30, 20);Use 30 pounds of Amazin’Oats and 20 pounds ofNutty Surprise. e. 50pounds

50

50

y

x


3-2 Part D

1. y5

x5

2. y5

x5

3. (0, 0), (0, 8), (4, 0)

10

10

y

x

4. (2, 0), 2, 4 12( ), (8, 0)

10

10

y

x

5. a. x ≥ 0, y ≥ 0, 50x + 25y ≤ 400, 2x ≥ 3y(or equivalent)b. 10

10

y

x

(0, 0), (6, 4), (8, 0)

c. P = 30x + 6yd. (8, 0); She shouldbuy 8 bags ofchocolate piecesand no bags ofpeppermint pieces.e. 240 pieces

CHAPTER 4

4-1 Part A

1. Yes; –2; –1;y10

x5n

an

0

2. Yes; 9, –32

3. No4. an = –1 + 3n5. an = 26 – 12n

6. an = –235

+ 35n

7. an = 8.75 – 0.75n

8. –213, 16

13

9. a. an = 21,500 + 1500n b. $32,000 c. 15th year

4-1 Part B1. 143 2. 195 3. 15,042 4. 250.46 5. 3166. 60 7. 600 8. –14,432 9. 552 10. 200

11. 5880 12. 1251 13. 24913 14. 154

15. 7n; 462n=1

11

∑ 16. 25 − 3n( )n=1

16

∑ ; –8

17. 5.2n −1.4( )n=1

25

∑ ; 1655 18. 113 − 6n( )n=1

33

∑ ; 363

19. 1680 20. a. $7.75 b. $107.50

4-1 Part C1. Yes; d = –6 2. No 3. No 4. Yes; d = –15. a. 34, 30, 26 b. 42, 80, 114, 144

6. 145, 152, 159, 166, 173 7. 5n + 2; 9270n=1

60

∑8. 882 9. –1155 10. 12,467 11. 522 12. 25813. –2450 14. a. $0.75 b. $2.75 c. $77.75

4-2 Part A

1. No 2. Yes; –1; –4 3. No 4. Yes; –13

; 581

5. Yes; 3; 27 6. No 7. an = 3(–2)n – 1

8. an = 100 15( )n−1

9. an = 7(−2)n−1.

10. an = 3(−1)n . 11. an = 640 12( )n−1

12. an = 27 43( )n−1

13. 168 14. 60 15. 120

16. 189 17. 40 18. 20 19. a. 131,072

b. 131,072 14( )n−1

20. 21, 63 21. 10,935

4-2 Part B

1. 6138 2. 63127128 or 63.9921875 3. 78,124

4. 9090.909091 5. 10,922 6. 11.4358881

7. 23433125

or 0.74976 8. 108.58515 9. 47,079,208

10. 415,9843125 or 133.11488 11. 4(−3)n−1

n=1

10

∑ ; − 59,048

12. 81,000 13( )n−1

; 121,481 1327

n=1

8

∑

13. 240 32( )n−1

; 4987 12

n=1

6

∑ 14. 256 − 34( )n−1

; 165 1316

n=1

7

∑

15. 7(4n−1); 152,915n=1

8

∑

16. 70(−0.1)n−1; 63.63n=1

9∑ 17. 7 −4( )n−1

n=1

8∑ ; –91,749

18. 4 19. 31,250 20. 42078 ft

4-2 Part C1. Yes 2. Yes 3. No 4. No 5. Yes 6. Yes

7. No 8. Yes 9. 47 10. 156

14 11. 1000 12. –40

13. –6034

14. 2412 15. 26

14 16. 41.1 or 41 1

9

17. 0.9n−1

n=1

∞∑ ; 10 18. 64 3

8( )n−1; 102 2

5n=1

∞∑

19. 10 − 45( )n−1

; 5 59

n=1

∞∑ 20. 256 − 1

4( )n−1; 204 4

5n=1

∞∑

21. 375 35( )n−1

; 937 12

n=1

∞∑ 22. 3

8( )n−1; 1 3

5n=1

∞∑

23. 2000 − 35( )n−1

; 1250n=1

∞∑ 24. 1

3( )n−1; 1 1

2n=1

∞∑

Answers


25. 0.6 + 0.06 + 0.006 + 0.0006; 23

26. 2 + 0.2 + 0.02 + 0.002; 209

27. 0.54 + 0.0054 + 0.000054 + ...; 611

28. 3.5 + 0.035 + 0.00035 + ...; 35099

29. 0.891 + 0.000891 + 0.000000891 + ...; 3337

30. 0.627 + 0.000627 + 0.000000627 + ...; 209333

31. 625 ft 32. 3712 in. 33. 170

23 cm2

4-2 Part D

1. Yes; –2; an = 3(–2)n – 1 2. Yes; 15; an = 1000 1

5( )n−1

3. a. 64, 96, 128, 160, 192 b. 64, 96, 144, 216, 324

c. 64, 160, 304, 520 4. 93468625

or 93.7488 5. 310,009

6. 25364

or 2.828125 7. 5115 8. 49,140 9. 46,116

10. 729 11. 25 12. 2113 13. –11

14

14. 5(7n−1)n=1

5

∑ 15. 343 − 27( )n−1

n=1

∞

∑16. 0.034 + 0.00034 + 0.0000034 + ...;

17495

17. a. 2000 + 2200 + 2420 b. 2000(1.1)n−1

n=1

20

∑c. $114,550

4-3 Part A

1. 7.2 2. 58 3. Commutative 4. Multiplicative

5. Closure 6. Possible answer: 27 ≠ 72 7. Possibleanswer: 3 ⋅ 4 is not an element of the set. 8. Possibleanswer: 3 ÷ 4 is not an integer. 9. a. Yes b. Yes;Additive identity is 0 and multiplicative identity is 1.c. Yes; 0 is its own inverse, 1 and 5 are inverses, 2 and 4are inverses, and 3 is its own inverse. d. No; 0, 2, and 4do not have inverses. e. No; 2 and 4 do not haveinverses under #. 10. No; The field axiom says thatnonzero numbers must have a multiplicative inverse.11. Distributive property of ⋅ over + .

4-3 Part B

1. Irrational 2. Rational; 32

3. Rational; –7

4. Rational; 45

5. √320.68; Irrational 6. 36; Rational

7. 5√ 2 8. 9√ 7 9. –20√10 10. 427

√ 6

11. x = ± 73 3 12. x = 1764 13. x = 729

5

14. x = ± 74 15. 2√15 16. –5√ 5 17. 3

2

18. 5√7h 19. x + 2 20. 5t2 21. About 7.30seconds

4-3 Part C

1. i√ 3 2. 40i 3. 10i√ 6 4. 23i 5.

58i 6. 1 5

7( )i7. 5i√ 3 8. 15i 9. 7 – 4i 10. 2 – 5i 11. i12. –1 13. 24 + 3i 14. 20 15. 40 + 42i

16. –20√ 3 17. –8i 18. –6 19. –21 20. 2 + 3i21. –3 + 2i 22. 4 – i 23. –17i 24. 42i25. –17 – 15i 26. 4 + 7i 27. 98 – 22i28. a. –4 – 11i b. 10 + 19i c. –18 – 41i, 38 + 79i29. a. 5 – 12i b. –119 – 120i, –239 + 28,560i

4-3 Part D

1. a. 3 + 4i b. 3i c. –1 – 2i d. 2 – 3i e. –4 + 3i2.–6.

imaginary5i

real5

6

2

3

4

5

7. 3 – 7i 8. –2 – 3i9. –4 + 7i 10. 6 + 5i11. 7 12. 12.5 13. 1314. 15

15. –2 – 3iimaginary

5i

real5

2 – 2i

–4 – i

16. 2 + 4iimaginary

5i

real5

5 + 3i

–3 + i

4-3 Part E

1. Commutative Property of Addition 2. ClosureProperty of Multiplication 3. Distributive Property ofMultiplication over Addition 4. Multiplicative identity5. Yes 6. Yes 7. No; Possible answer: 2 does nothave a multiplicative inverse in the set 8. No; Possibleanswer: 1 + 1 = 2, so the set is not closed under addition.9. Complex 10. Imaginary, complex 11. Real,complex 12. Real, complex 13. 9i 14. 5 2 n15. –7

8 16. 31 – i 17. 10 + 8i 18. 10 – 5i

19. 243i 20. –5√11 21. 7 – 9i 22. –3 – 2i23. –14i 24. –5 + 8i 25. 102; Rational


CHAPTER 5

5-1 Part A

1. 32 ,94( ) ; x = 3

2;

Maximum y = 94

y5

x50

2. (–1, –4); x = –1;Minimum y = –4

y5

x50

3. x = 4 4. x = 32 5. x = 5.7 6. x = –5.4

7. Possible Answer: (4, 20) 8. Possible Answer: (2, 5)9. Possible Answer: (3, 3)10. Possible Answer: (–1, 26) 11. (–2, –3); x = –2;(0, –1); Minimum y = –3 12. (4, 4); x = 4; (6, –4);Maximum y = 4 13. Not quadratic14. Quadratic; y = x2 – 2x – 1515. Quadratic; y = 2x2 – 10x + 20 16. Not quadratic

5-1 Part B1.

y5

x50

f(x)

g(x)

2.y

5

x50

f(x)

g(x)

h(x)

3. y = 7x2 4. y = –2x2 5. y = –2x2 6. y = 32x2

7. y = –4x2 8. y = 25x2 9. y = –1

3x2; y =

13x2

10. y =35x2; y = –3

5x2 11.a. K(v) = 3

2v2 b. The graph of

K(v) is narrower. c. 32

Joules, 6 Joules, 24 Joules,

96 Joules d. 6 m/s

5-1 Part C

1. a. 3 2. 2 c. 1 d. 42.

y5

x5

0

f(x)

g(x)

3.y

5

x50

g(x)

h(x)

f(x)

4. (0, 0); Maximum 5. (3, 5); Minimum 6. (–2, 3);Maximum 7. (2, –4); Minimum 8. (–7, –17);

Minimum 9. π, 78( ); Maximum

10. f(x) = 5(x – 2)2 + 3 11. f(x) = –3(x + 2)2 + 7

12. f (x) = − 29 x − 3

7( )2+ 4

9 13. f x( ) = 23 x − 7( )2 − 3

214. f(x) = m(x – c)2 + d 15. f(x) = p2(x – 3m)2 + 2n16. Translate 3 units right and 5 units upward.17. Reflect over x-axis and translate 2 units left.18. Reflect over x-axis and translate 5 units left and 3 unitsdownward. 19. Translate 4 units left and 11 unitsupward. 20. Reflect over x-axis and translate 7 unitsdownward. 21. Translate 8 units right and 17 unitsdownward.

5-1 Part D1. 9 2. 4 3. –22n 4. 0.09 5. 400 6. –5z

7. 26m 8. 625 9. –67x 10.

12125

11. y = (x + 4)2 – 16; (–4, –16); x = –4; Minimum y = –1612. y = (x – 5)2 –25; (5, –25); x = 5; Minimum y = –2513. y = (x – 2)2 – 16; (2, –16); x = 2; Minimum y = –16

14. y = x + 52( )2

− 254 ; − 5

2 ,− 254( ); x = –5

2;

Minimum y = –254

15. f(x) = (x + 1)2 – 8; (–1, –8); x = –1; Minimum f(x) = –816. f(x) = (x – 3)2 + 3; (3, 3); x = 3; Minimum f(x) = 3

17. h x( ) = 3 x + 32( )2

− 274 ; − 3

2 ,− 274( ); x = –

32; Minimum

h(x) = –274 18. g(x) = 4(x – 8)2 – 241; (8, –241); x = 8;

Minimum g(x) = –241 19. h = −6 t − 76( )2

+ 496 ; 7

6 , 496( );

x = 76; Maximum h = 49

6 20. h = –1

2(t + 8)2 + 44; (–8, 44);

x = –8; Maximum h = 4421.a.

y5

x50

b. Yes, x = 2; Possibleanswer: The graphsintersect atx = 2.

5-1 Part E1. Possible answer: (4, 5) 2. Possible answer: (3, 8)3. Possible answer: (11, 6) 4. Possible answer: (–11, 5)5. Possible answer: (5, 0) 6. Possible answer: (–8, –9)7. (0, –21); x = 0; Minimum 8. (7, –18); x = 7;Maximum 9. (–2, –5); x = –2; Minimum 10. (3, 7);t = 3; Maximum11.

y5

x50

f(x)g(x)

h(x)

12.y

5

x50

f(x)

g(x)

h(x)

13. y = (x – 2)2 + 11; (2, 11); x = 2; Minimum y = 11

14. g(x) = 12(x + 7)2 –271

2 ; −7, − 27 1

2( ); x = −7;

Answers


Minimum y = –2712 15.a. h t( ) = −16 t − 3

8( )2+ 7 1

4

b. 38 sec c. 7 ft 3 in.

5-2 Part A

1. 1 2. 03. x = 2 or x = 4

y5

x50

4. x = –4 or x = 0y

5

x50

5. 0 = 2x2 – 10x – 7 6. 0 = 3x2 – 6x – 27. 0 = 3x2 – 5x + 3 8. 0 = x2 – 16x + 649. 0 = 6x2 – x – 15 10. 0 = x2 – 3x – 811. x = –1 or x = 3

y5

x50

12. x < –2.2 or x < 0.7y

5

x50

5-2 Part B

1. D 2. B 3. F 4. A 5. E 6. C 7. x = –2 or

x = 0 8. x = 2 or x = 4 9. x = –3 or x = –5

10. x = 2 or x = 8 11. x = –1 or x = 4 12. x = 3 or

x = 7 13. Cannot be solved by factoring

14. x = –37 or x = –2 15. x = 1 or x = 5

4 16. x = –1 or x

= 9 17. Cannot be solved by factoring 18. x = –23 or

x = 5 19. x = –5 or x = –34 20. Cannot be solved by

factoring 21. x = –7 or x = 7 22. x = –5 or x = 5

23. x = –0.4 or x = 0.4 24. x = –0.8 or x = 0.8 25. x <–2.9 or x < 2.9 26. x < –1.9 or x < 1.9 27. w = 4 ft

5-2 Part C

1. x = 12

or x = –3 2. x = −5+ 332 or x = −5− 33

2

3. y = −3−i 234 or y = −3+i 23

4 4. x = −1−i 113 or

x = −1+i 113 5. x = 1− 7 or x = 1+ 7

6. m = 5− 132 or m = 5+ 13

2 7. x < –6.77 or x < 1.77

8. y < 0.31 or y < 9.69 9. x < 0.63 or x< 2.3710. x < –1.60 or x < 1.10 11. x < 0.18 or x < 1.2312. x < –1.98 or x < 0.64 13. x < –0.88 or x < 1.3014. n = –1 or n = –0.17 15. x = –24 or x = 2016. w < –0.68 or w < 5.18 17. x < –0.52 or x < 3.1918. x < –7.11 or x < 2.11 19. t < –2.24, t = –1, t = 1,or t < 2.24 20. u < –2.14i, u < –0.66i, u< 0.66i, oru < 2.14i 21. r < 3.14 cm 22. a. At t < 0.3 sec andat t < 2.8 sec b. At t < 3.1 sec 23. 3.2 cm; 8 cm

5-2 Part D

1. 0; < 0 2. 1; = 0 3. 2; > 0 4. Two real solutions5. One real solution 6. Two complex-number solutions7. Two real solutions 8. Two real solutions9. Two complex-number solutions 10. Two 11. Two12. None 13. One 14. Two 15. Two16. Possible answer:

y5

x50

17. Possible answer:y

5

x50

18. No real solutions, because we need to solve–4.9t2 + 3t – 0.5 = 0, and the discriminant is –0.8.

5-2 Part E1. x = –3 or x = –1

y5

x50

2. x = –3 or x = 5y

5

x50

3. x = –4 or x = –1; Possible answer: Use factoring becausethe equation factors. 4. y < 0.4 or y < 5.6; Possibleanswer: Use the quadratic formula because the equationdoes not factor. 5. u = –2 or u = 5; Possible answer:Use factoring because the equation factors. 6. x = –2.5or x = 1; Possible answer: Use factoring because theequation factors. 7. x < 0.4 or x < 1.4; Possibleanswer: Use the quadratic formula because the equationdoes not factor. 8. u = 3 or u = 7; Possible answer: Usefactoring because the equation factors 9. x < –1.3 orx < –0.2; Possible answer: Use the quadratic formulabecause the equation does not factor. 10. x < –1.7 or x< 1.2; Possible answer: Use the quadratic formula because

the equation does not factor. 11. x = –23 or x = 3

4

12. x = 2 – 3i or x = 2 + 3i 13. x = –3 or x = 12

14. x = –53 or x = 1 15. x = –

34–

√47i4

or x = –34 +

√47i4 16. x = –2 – 2√ 3 or x = –2 + 2√ 3

17. Two real solutions 18. Two complex-numbersolutions 19. Two complex-number solutions20. One real solution 21. Two complex-numbersolutions 22. Two real solutions23. –23 and –21, or 21 and 23 24. a. At about 3.19 secb. At about 6.39 sec

5-3 Part A

1. x2 + y2 = 16 2. (x + 3)2 + (y – 1)2 = 25


3.y

5

x50

4.y

5

x5

5. 5 6. 10.82 7. 51 8. 19.109. (x – 4)2 + (y – 8)2 = 9 10. (x + 2)2 + (y – 7)2 = 1311. (x – 2)2 + (y + 4)2 = 146 12. (x + 3)2 + y2 = 16;

(–3, 0); 4 13. x2 + (y + 7)2 = 12; (0, –7), 2√ 314. (x – 4)2 + (y + 3)2 = 25; (4, –3); 5

15. (x + 6)2 + (y – 3)2 = 19; (–6, 3); √19

5-3 Part B

1. (0, –√ 5) and (0, √ 5)y

0

5

x5

2. (–√13, 0) and (√13, 0)y10

x100

3. x2

9 + y2

16 = 1 4. . x2

64 + y2

25 = 1 5. 0.80 6. 0.38

7. x−3( )2

16 + y2

25 = 1; (3,0) 8. x2

4 + y+1( )2

16 = 1; (0, –1)

9. x+5( )2

16 + y−3( )2

9 = 1; (–5, 3) 10. x−7( )2

64 + y+2( )2

25 = 1;

(7, –2)

11. y = ±4 1− x29

y

0

5

x5

Possible answer:−5 ≤ x ≤ 5, − 5 ≤ y ≤ 5

12. y = ±5 1− x236

y

0

10

x10

Possible answer:−10 ≤ x ≤ 10, −10 ≤ y ≤ 10

5-3 Part C

1. (–√13, 0) and (√13, 0);

y = –32x and y = 3

2 x

y5

x50

2. (0, –√34) and (0, √34);

y = –35x and y =

35x

y10

x100

3. 8 4. 10 5. 10 6. 18

7. (–1, 1); (–1 – √10, 1)

and (–1 + √10, 1)y

5

x50

8. (2, 3); (2, –2) and (2, 8)y

10

x100

9. (x – 2)2

9 – y2

16 = 1; (2, 0) 10. (x+2)2

49 − y2

25 = 1; (–2, 0)

11. y2

16 – (x + 7)2

4 = 1; (–7, 0)

12. y+1( )2

49 − x−4( )2

16 = 1; (4, –1)

5-3 Part D1. y = –2(x – 2)2 + 3 2. (x – 3)2 + (y – 7)2 = 29

3. x2

9 + y2

25 = 1 4. x2

16 – y2

9 =1

5. Circle; (–2, 1); 3y

5

x50

6. Hyperbola; (0, 1);(–2, 1) and (2, 1)

y5

x50

7. Parabola; (3, 2)y

5

x50

8. Ellipse; (1, 0);(1, –3) and (1, 3)

y5

x0 5

9. y = 3(x – 2)2 – 5; Parabola; (2, –5) (vertex)

10. x−3( )24 − y+2( )2

9 = 1; Hyperbola; (3, –2)

11. x+6( )2

16 + y−4( )236 = 1; Ellipse; (–6, 4)

12. (x – 5)2 + (y – 3)2 = 25; Circle; (5, 3)

Answers


5-4 Part A1. (–1, 1), (3, 1)

y5

x50

2. (–3, 4), (4, –3)y

5

x0 5

3. (–3.4, –1.6), (0, 3)y

5

x0 5

4. (3, –5), (3, 5)y

10

x100

5. (–2, –1) 6. (–√ 2, –2√ 2), (√ 2, 2√ 2)7.

y5

x0 5

8.y

5

x0 5

5-4 Part B1. (1, 0), (4, 3)

y5

x50

2. (–1, 2), (2, 0)y

5

x0 5

3. (–3, 4), (0, –5), (3, 4)y

5

x50

4. (–2.5, –2.3), (–2.5, 2.3),(2.5, –2.3), (2.5, 2.3)

y5

x50

5. (–2, –1), (–2, 1), (2, –1), (2, 1) 6. (–4, 2)7. (–1, 3), (1, 3) 8. (–3, –2), (–3, 2), (3, –2), (3, 2)

9.y

x0 5

5

10.y

x0 5

5

5-4 Part C1. (–1, –4), (1, 0)

y5

x50

2. (0, –3), (3.2, 1.8)y

x0 5

5

3. (–2, 0), (2, 0)y

x0 5

5

4. (–2.1, 2.4), (0, –2),(2.1, 2.4)

y5

x50

5. (0, –2), (4, 26) 6. (–4, 2), (4, –2) 7. (–√15, 7),

(0, –8), (√15, 7) 8. (–2, –3), (–2, 3), (2, –3), (2, 3)9.

y

x0 5

5

10.y

x0 5

5

CHAPTER 6

6-1 Part A

1. 6 2. 120 3. 5040 4. 718 5. 1446. 40,320 7. 1 8. 362, 856 9. a. 3 b. 5 c. 810. a. 2 b. 32 c. 16,384 d. 524,288 11. a. 3b. 2 c. 6 12. a. 17,576,000 b. 11,232,00013. 12

Soup

Quiche Chicken Fish

Cake Pie Cake Pie Cake Pie


Salad

Quiche Chicken Fish

Cake Pie Cake Pie Cake Pie

6-1 Part B

1. AH, AL, AP, AR, HA, HL, HP, HR, LA, LH, LP, LR,PA, PH, PL, PR, RA, RH, RL, RP 2. 24 3. ORSS,OSRS, OSSR, ROSS, RSOS, RSSO, SORS, SOSR,SROS, SRSO, SSOR, SSRO 4. 120 5. 120 6. 427. 60 8. 20,160 9. 12 10. 7980 11. 15,12012. 360 13. 20,160 14. 50,400 15. 20,16016. 30,240 17. 60 18. 72 19. 1,396,755,36020. a. 864 b. 480 21. 420 22. 32,432,400

6-1 Part C1. 24 2. 303,600 3. 7,893,600 4. 5040 5. 21606. 744 7. 144 8. 60 9. 6720 10. 6 11. 84012. 7213. 18

Blue

1 2 3 4 5 6

Green

1 2 3 4 5 6

Red

1 2 3 4 5 6

14. 6 15. 907,200 16. 3360 17. 10,08018. a. 3 b. 2 c. 1 d. 6 19. 5040 20. 2520

6-2 Part A1. 9880 2. 184,756 3. 30 4. 200 5. 6,724,5206. 6435 7. 455 8. 21 9. 201,376 10. 5005

11. 210 12. 3366,640 < 0.0005 13. 252 14. a. 36

b. 84 c. 126 15. 22,544,815 < 8 3 10–7 16. 120

17. a. 303,600 b. 12,650

6-2 Part B1. 126x5y4 2. –35x4y3 3. 1792x6y2

4. –145,152x6y3 5. x7 + 7x6y + 21x5y2 6. 65,536 –131,072y + 114,688y2 7. x5 – 5x4y + 10x3y2 – 10x2y3 +5xy4 – y5 8. x7 + 21x6 + 189x5 + 945x4 + 2835x3 +5103x2 + 5103x + 2187 9. 256x8 – 1024x7y + 1792x6y2

– 1792x5y3 + 1120x4y4 – 448x3y5 + 112x2y6 – 16xy7 + y8

10. x5 – 10x4y + 40x3y2 – 80x2y3 + 80xy4 – 32y5

11. 4096u6 – 18,432u5v + 34,560u4v2 – 34,560u3v3 +19,440u2v4 – 5832uv5 + 729v6 12. 16a4 + 160a3b +600a2b2 + 1000ab3 + 625b4 13. –32t5 + 240t 4u –720t3u2 + 1080t2u3 – 810tu4 + 243u5 14. 14 15. 2616. 5 17. About 0.138 18. h6 + 6h5t + 15h4t2 +

20h3t3 + 15h2t4 + 6ht5 + t 6 a. 64 b. 15 c. 1 564

d. 22 e. 1132

6-2 Part C

1. 210 2. 10 3. 56 4. 66 5. 1 6. 4557. 220 8.

11850 < 0.013 9. 35 10. 13,991,544

11. 165 12. 175 13. x7 + 7x6y + 21x5y2 + 35x4y3 +35x3y4 + 21x2y5 + 7xy6 + y7 14. 64x6 – 192x5y +240x4y2 – 160x3y3 + 60x2y4 – 12xy5 + y6 15. 1024a5 +3840a4b + 5760a3b2 + 4320a2b3 + 1620ab4 + 243b5

16. 15,625c6 – 131,250c5d + 459,375c4d2 – 857,500c3d3 +900,375c2d4 – 504,210cd5 + 117,649d6 17. m7 + 35m6n+ 525m5n2 + 4375m4n3 + 21,875m3n4 + 65,625m2n5 +109,375mn6 + 78,125n7 18. x6 – 42x5 + 735x4 – 6860x3

+ 36,015x2 – 100,842x +117,649 19. 28,160x9y2

20. 28u2v6 21. 0.3125

CHAPTER 7

7-1 Part A

1. 4 2. 23 3. 5 4. 1

3 5. 2 6. 3 7. 40 8. 4

9. 64 10. 52 11. 120 12. 1000 13. t is doubled14. t is divided by 4. 15. t is multiplied by 8.16. t is divided by 8. 17. V varies directly with the cubeof r. 18. A varies jointly with l and w. 19. r variesdirectly with C. 20. D varies directly with the square of t.

21. a. E = kmv2 b. k = 12 c. E = 40

7-1 Part B

1. Graph 1 is y = x6 and graph 2 is y = x4, because graph 1is steeper for x > 1. 2. Graph 1 is y = x9 and graph 2 isy = x8, because graph 1 must be the graph of a functionwith an odd exponent.3. y

5

0x

5

y = x3

y = x2

4. y20

0 x20

y = x5y = x7

5. 6.

7. a. Quadratic, 10 is even. b. Line symmetry, the graphis symmetric about the y-axis. c. More steeply

7-1 Part C

1. False; 22 ⋅ 23 = 25 2. True; Power of Quotients

3. False; (3 ⋅11)4 = 34 ⋅114 4. True; Power of Powers

5. True; Quotient of Powers 6. False; (32 )4 = 38

7. 125x3 8. 1

125x3 9. 1t 10. −1024t10

11. 16x4 12. 81a4b8c12 13. y2

x2 14. 24x11

15. 1

b4c8 16. − u6

64t 9 17. 3x4z8

4y7 18. 13w12

17u13v7

19. 602,000,000,000,000,000,000,00020. 300,000,000 m/sec

21. 73,500,000,000,000,000,000,000 22. 1.5 ×1011 m

23. 6.371 ×106 m 24. 1.75 ×1012 hours

25. 7.68 ×102 26. 1.404 ×1021 27. 1.5 ×10−7

28. 2.5 ×1013 29. 1.778 ×1026 30. 7.4088 ×10−17

31. 2.4 ×10−14 mi3

Answers


7-1 Part D

1. 60 2. 5 3. 32 4. 63 5. 24 6. 196

7. y5

0 x5

y = x7

y = x8

8. y5

0 x5

y = 2x3

y = x4

9. 1

8d3 10. 49d 4

e8 11. 72x7 12. y8

4z

13. 2.736 ×10−14 14. 5 ×1034 15. 5.23 ×10−9

16. 3.8576 ×1011 17. 283,000,000 18. 0.000 0375

19. a. t = k dr b. k < 0.8696 c. 10 hours

7-2 Part A

1. 34 2. 493 3. 121/5 4. z5/3 5. 1

(3+ x )34

6. 2xy 7. 35/ 4 p5/ 4q5/ 4 8. x2/3y 9. y107

10. 9a2b43 11. a1/2b3/2 12. x2y4z6

13. Does not exist 14. Positive 15. Negative16. Positive 17. Negative 18. Does not exist

19. 9 20. 11024

21. 3 22. 7 23. 32 24. 81

25. 729 26. 13125

27. 128 28. 2187

29. x (x ≥ 0) 30. p3 31. 25 32. x12

33. 193 34. √ 2 35. x320 36. 1

5 37. 1

66 38. 164

7-2 Part B1. Power regression 2. Linear regression 3. 16.724. 0 5. 64 6. 1 7. 24.19 8. 0.03 9. 1025.86

10. 0.93 11. x7.53 12. y15.12 13. p6.7

14. r−6.2 15. a9.3b4 16. c0.84d8.25 17. s27t−35

18. t10.78

19. a.y

200

160

120

80

40

0 2 4 6 8x

10

b. A = 1.21465 B = 2.41725c. 38.99

7-2 Part C1. x = 10 2. x = 17 3. x = 4 4. x = 50 5. x = 96. x = 21 7. x = 20 8. x = 6 9. x = 5 10. x = –1or x = –2 11. x = 6 12. x = 16 13. x = 2714. x = 7 15. x = 9 16. x = 10 17. x = 918. x = –65 19. x = 36 20. x = –32 or x = 3221. x = 11 22. x = 8 23. x = –125 or x = 125

24. x = 19 25. y = − 2x12 or y = 2x

12 26. t = s2

27. x = y2/3 28. x = 32 y3 29. D = 16t2

30. a = 6.25 ×10−12 b2 31. u = 12 2 v4

32. x = z3

8y 33. x = −y3/ 4 or x = y3/ 4

34. s = −t5/ 4 or s = t5/ 4 35. a. r = Ap

n − 1

b. About 7.96% 36. a. r = 3V4π

3 b. About 1.89 cm

7-2 Part D1. x < 0.41

y5

0 x5

2. x < 0.66y

5

0 x5

3. x = 8 4. x = 8 5. x = 4 6. x = 12 7. x = 488. x = 8 9. No 10. Yes 11. Yes 12. No13. Yes 14. Yes 15. x = 16 16. x = –27 or= –64 17. x < 1.68 18. x = 9 or x = 2519. x < 2.52 or x < 8.55 20. x < 1.18

21. y = − 16 x + 4

3

7-2 Part E1. –2 2. 3 3. 49.01 4. 0.2 5. 1024 6. 29.96

7. 9 8. 256 9. x1712 10. x158 11. a6.1

12. z5.19 13. x15 14. x53 15. c4.86d6.84

16. m6.3n0.5 17. x = 47 18. x = 20 19. x = 320. x = 5 21. x = 4 22. x = –2 23. x = –2 or x = 2224. x = 4 25. x = 6 26. x = 2 27. x = –27, x = –1,x = 1 or x = 27 28. x = 9 29. x < 2.08 or x < 2.9230. x = –32 or x = 32 31. x = 1 32. x < –3.17 or

x < 14.62 33. 7% 34. v = ± 2Em 35. y = 3x2

z3

7-3 Part A

1. 13 2. 19 3. 85 4. –4 5. t2 + 1

6. a2 + 2a − 2

7. y5

0 x5

f (x)

(f + g)(x)

g(x)

8. y5

0 x5

f (x)(f + g)(x)

g(x)

9. (f + g)(x) = 8; (f – g)(x) = 2x – 2;

( f ⋅ g)(x) = −x2 + 2x + 15 10. (f + g)(x) = x2 + 2x;

(f – g)(x) = x2 – 2x; ( f ⋅ g)(x) = 2x3

11. ( f + g)(x) = 3x2 + 5x + 2; ( f − g)(x) = 3x2 + 5x − 2;

( f ⋅ g)(x) = 6x2 + 10x 12. (f + g)(x) = 5x – 4;


(f – g)(x) = –x – 6; ( f ⋅ g)(x) = 6x2 − 13x − 5

13. ( f + g)(x) = x2 − 2x + 5; ( f − g)(x) = x2 + 2x + 5;

( f ⋅ g)(x) = −2x3 − 10x

14. ( f + g)(x) = x2 + 4x − 1; ( f − g)(x) = x2 − 2x + 1;

( f ⋅ g)(x) = 3x3 + 2x2 − x 15. a. 7 b. –2 c. 1d. 12 e. 35 f. 8

7-3 Part B

1. 4 2. 7 3. 25 4. 19 5. x4 6. 2x2 + 17. 10; 16 8. 2; 5 9. –8; 58 10. 7; 11 11. 30; 1412. 6; 0 13. 2x + 4; 2x + 11 14. 15x + 17; 15x – 19

15. x2 ; x2 + 2x 16. x12 ; x12 17. x2 + 3x + 2;

x2 − x + 2 18. x; x 19. x4 20. x + 6 21. 2x

22. x2 + 6x + 9 23. 4x2 − 12x + 12 24. 2x2 + 3

25. a. r = 3V4π

3 b. r = 45t2π

3 c. After 241 sec or

about 4 min

7-3 Part C

1. y5

0 x5

2. y5

0 x5

3. y5

0 x5

4. y5

0x

5

5. f(g(x)) = (x – 7) + 7 = x √; g(f(x)) = (x + 7) – 7 = x√6. f(g(x)) = 2 1

2 x − 52( ) + 5 = x√;

g( f (x)) = 12 (2x + 5) − 5

2 = x √

7. f (g(x)) = 3 x−93( ) + 9 = x √; g( f (x)) = (3x+9)−9

3 = x √

8. f (g(x)) = (x3 − 7) + 73 = x33 = x √;

g( f (x)) = x + 73( )3− 7 = (x + 7) − 7 = x √

9. f −1(x) = x + 3 10. f −1(x) = 14 x + 2

11. f −1(x) = 15 x − 4 12. f −1(x) = x3 − 1

13. f −1(x) = x5

2 14. f −1(x) = 1x3

7-3 Part D

1. –13 2. –10 3. 36 4. –2 5. −4x2 + 20x − 25

6. −2x2 − 5 7. −x2 + 2x − 5 8. −x2 − 2x + 5

9. −2x3 + 5x2 10. x2 + 2x − 5 11. –37; –43

12. –4; 4 13. 912; 141

2 14. 8; 122

15. –9x + 14; –9x + 28 16. x + 6; x + 3

17. x2 − 8x + 16; − x2 + 4 18. x2 − 14; x2 + 6x − 8

19. f (g(x)) = −2 − 12 x − 3

2( ) − 3 = x + 3 − 3 = x √

g( f (x)) = − 12 (−2x − 3) − 3

2 = x + 32 − 3

2 = x√y

5

0 x5

20. f (g(x)) = ( x − 23 )3 + 2 = (x − 2) + 2 = x √;

g( f (x)) = (x3 + 2) − 23 = x33 = x√y

5

0 x5

21. f −1(x) = 13 x − 4 22. f −1(x) = 5 − x

23. f −1(x) = −2x + 6 24. f −1(x) = 12 x3

25. f −1(x) = x3 − 2 26. f −1(x) = x3 − 6x2 + 12x − 8

CHAPTER 8

8-1 Part A1. C, equation is quartic. 2. D, equation is cubic withpositive leading coefficient. 3. A, equation is cubicwith negative leading coefficient 4. B, graph is a

parabola. 5. x5 − x4 + x3 + x2 + 10x − 8;

x5 + x4 − 5x3 + 5x2 − 6x − 2

6. 7x5 + 2x4 − x3 + 5x2 − 8x + 10;

−7x5 + 2x4 − 5x3 + 5x2 + 8x + 6

7. 7x3 − 2x − 5; − x3 + 4x2 − 8x + 11

8. 4x6 − 4x3 + 7x2 − 1; 4x6 − 6x4 + 4x3 − 3x2 − 1

9. x2 + 8x + 10; 1; 2 10. 3x3 + 7x2 − 6x; 3; 3

11. 16x + 16; 16; 1 12. 2x3 + 8x2 − 6x − 24; 2; 3

8-1 Part B

Given intervals are possible answers.1. None; None; 3.1 between x = –1 and x = 0; –3.9between x = 1 and x = 2 2. None; –8.2; 6.6 betweenx = –1 and x = 0; 3.7 between x = –2 and x = –1

3. None; None; 0.0 between x = − 12 and x = 1

2 and 4.2

between x = –3 and x = –2; –0.2 between x = –1 and 0 and–2.5 between x = 1 and x = 2 4. 3.9; None; –1.6between x = –2 and x = –1; –4.0 between x = –1 and x = 0

8-1 Part C1. –4, –1, 1, 3 2. –2, 1, 4 3. –7, –2, 4, 7 4. –4, 55. –3, 0, 4; Possible answer: Factoring 6. –3, 0, 3;Possible answer: Factoring 7. 1, 2; Possible answer:

Answers


Factoring 8. − 72 ; 3; Possible answer: Factoring

9. 5− 132 , 5+ 13

2 ; Possible answer: Quadratic formula

10. None; Possible answer: Discriminant is negative.

11. 0, 23

, 1; Possible answer: Factoring 12. –3 – √ 5,

–3 + √ 5, 0; Possible answer: Factoring and quadraticformula 13. None; Possible answer: Discriminant is

negative. 14. − 12 , 0, 3; Possible answer: Factoring

8-1 Part D

1. 3x4 + x3 + x2 − 3x + 9; 3x4 − 5x3 + x2 + x − 1

2. −4x5 + 2x4 + 6x3 − 7x2 + 7x − 1;

− 4x5 − 2x4 + 6x3 + 3x2 + 3x + 1 3. x2 − 6x; 1; 2

4. 2x3 − 2x2 − 60x; 2; 3 5. 2x2 + 6x + 5; 2; 26. None; None; Possible answer: 4.1 between x = –2 andx = –1; Possible answer: –2.5 between x = 2 and x = 3; –3,1, 4 7. None; –0.6; Possible answer: 0.2 between x = 2

and x = 3; Possible answer: 0 between x = 112 and x = 21

2; 2,

3, 4 8. –7, 0, 2 9. –7, 0, 7 10. –3, 0, 52

11. 0, 3− 152 , 3+ 15

2

8-2 Part A

1. − 23

y5

0 x5

2. 1, 4y

5

0 x5

3. x < –3.4 4. x < –6.2, x = 2 5. x = –3, x = 0 or x =2 6. x < –2.4, x = –2, or x < 5 7. x < –2.4,x < –0.4, or x < 3.9 8. x < –2.7, x = 0, or x < 3.79. x < –3.1, x < 0.8, or x < 3.3 10. x < –3.4, x = 2, orx < 2.4 11. x < –1.6 or x = –1 12. x < –1.9 orx < –0.5 13. x < –2.0, x < –0.2, x < 1.3, or x < 1.814. x < –2.0 or x < 2.1

8-2 Part B

1. x = –2, x = 0, or x = 5 2. x = 2, x = –1 + √ 3i, or

x = –1 – √ 3i 3. x = –4, x = 0, or x = 14. x = –2, x = 2, x = –2i, or x = 2i5. x = 0, x = 3, or x = 5 6. x = –4, x = 4, x = i, or x = –i7. x = 0 or x = 2 8. x = –3, x = –1, or x = 1

9. x2 + 3x − 4; 0 10. x2 − 2x + 5; − 2

11. x2 + 3x − 6; − 10 12. x2 − 5x + 7; 6

13. x3 − 4x2 + x + 3; 0 14. 2x2 − 5x + 3; − 215. –4 16. 343 17. 91 18. 3 19. –14

20. –9 21. 6x2 − 17x − 9 22. –423. Possible answer: It is not a factor because P(−2) ≠ 0.24. Possible answer: P(x) = x(x + 1)(x − 3)(x − 5)

25. Possible answer: (x − 4)(x2 − 4x + 29) = 026. 6 in.; 15 in.; 8 in.

8-2 Part C1. Yes; x = –2; 5 2. No; 3 3. No; 3 4. Yes; x = 1and x = 2; 6 5. Yes; x = –1; 4 6. Yes; x = 0; 67. Yes; x = –3; 4 8. Yes; x = 5; 3 9. No; 610. No; 6 11. x = –5, x = 1, or x = 3 12. x = –5, x =

–2, or x = 1 13. x = 12 or x = 3 14. x = –5, x = 1, or

x = 2 15. x = –2, x = –1, x = 2, or x = 3 16. x = –4,

x = 1, or x = 32

17. x = 12, x = 1, x = –4i, or x = 4i

18. x = –3, x = –2, x = 13 , or x = 3 19. x = 3

5, x = 1, or

x = 2 20. x = 2, x = 52, x = –2i, or x = 2i 21. –1, 1, –2,

2, –5, 5, –10, 10 22. − 15 , 1

5 , − 25 , 2

5 , − 1, 1, – 2, 2

8-2 Part D1. x < 0.6, x < 1.7, or x < 4.7 2. x < 0.2, x < 2.5, or

x < 4.3 3. x = 0, x = 3, or x = 4 4. 2x2 − 5x + 3; − 2

5. 2x2 − 4x + 7; 0 6. 3x3 + 2x2 − 5x + 8; − 3

7. 4x3 − 5x2 + 7x − 8; 10 8. 21 9. 37 10. –911. 106 12. –47 13. –30

14. P(x) = 12x2 + 7x − 3 15. x + 3 is a factor of R(x).

16. Possible answer: (x − 3)3(x − 6)(x − 8) = 0

17. − 16 , 1

6 , − 13 , 1

3 , − 12 , 1

2 , − 1, 1 18. x = –5, x = 0,

or x = 3 19. x = –6, x = 6, x = –i, or x = i 20. x = 1,x = 2, x = 3, or x = 4 21. x = –5, x = –2, x = 0, or x = 5

22. x = 32, x = 2, or x = 5 23. x = –3, x = 1, x = 2, or x = 6

8-3 Part A

1. 117 2. − 16

5 3. 1417 4. 1

2 5. − 37 6. 9

7

7. 29 8. 19

6 9. 211 10. –2 11. –4i

12. –1.2 + 1.6i 13. –3 – i 14. 5 – 2i 15. 0.9 + 1.2i

16. –1.28 + 1.04i 17. 113 + 21

13 i 18. 1334 − 33

34 i

19. − 3x3

2y2 20. 4a5

11b4 21. a + 3 22. 2x+13x+5

23. (x+2)(x+3)x+5 24. 4xy5

7z9 25. (x+2)(x+3)(x−4)2x+3

26. 1(x−3)(x+1) 27. y(y+1)

3(y+5) 28. 1(m−3)(m+1)

30. a. 3.84 + 2.88i ohms b. 9613 − 90

13 i ohms

c. 2.4 ohms d. 0.24 + 4.32i ohms

8-3 Part B

1. 15x2 2. 162u7 3. 2(z + 2)(z – 2)4. (a + 3)(a – 3) 5. (x – 2)(x + 3)(x + 4)6. (v – 6)(v – 3)(v + 6) 7. 4(c – 3)(c + 7)8. (t – 5)(t + 2)(t + 6) 9. 6(x – 4)(x – 1)(x + 4)

10. (w – 5)(w + 2)(2w + 3) 11. 4x2 +14x−3

6x2

12. − 10v2 +33v+8

20v3 13. 3y2 +5y−42y(y+2) 14. 8t+1

t+3


15. 2 16. 4w(2w+7)(w+3)(w+5) 17. −6

(z+3)(z−3)

18. 4x2 −6x+10(x+2)(x+1)(x−3) 19. 3a2 −3a−4

2(a+3)(a+4)

20. t3 −5t2 −15t−17(t−3)(t+2)(t+5) 21. 6r2 +17r+2

4(r+3)(2r−1) 22. 9a+146(a+5)

23. a. 80

w2 +w b. 4 in. 24. a. −6000

x2 −625 b. 10

c. 15 d. –21.8; No, the current is too fast, so the boatwill not be able to return.

8-3 Part C

1. x = 3.5 2. x = –4, x = 4 3. x = –1, x = 3 4. x = 0,x = 5 5. x = − 3

2 , x = 7 6. x = –2, x = 0, x = 57. Asymptote at x = 2; Possible answer:

x –3 –1 0 1 3 4y − 1

5 − 13 − 1

2–1 1 1

2

y5

0 x5

8. “Hole” at x = 3; Possible answer:x –2 –1 0 1 2 4y 2 2 1

23 3 1

24 5

y5

0 x5

9. Asymptote at x = –2 and “hole” at x = 3;Possible answer:

x –3 0 1 2 4y –2 1 2

312

13

y5

0 x5

10. Asymptotes at x = –3 and x = 1; Possible answer:x –4 –2 –1 0 2 3y 4

5 − 23 − 1

40 − 2

5 − 14

y5

0 x5

8-3 Part D

1. x = 136 2. x = 72

5 3. a = − 32 or a = 4

4. x = − 73 or x = 3 5. x = 13

4 or x = 8

6. z = 1 or z = 6 7. c = 1 or c = 9 8. x = –19. All real numbers except –3 and 2 10. x = 6 or x = –911. x = 5 12. x = 1 or x = 4 13. x = 3 14. x = –9 or

x = 5 15. x = 5 or x = 22 16. x = − 72 , x = 0, or x = 4

17. x = − 54 or x = 3 18. x = − 5

2 or x = 8 19. x = –5

or x = 4 20. x = –2 or x = 3 21. a. 84 ohmsb. 15 ohms, 10 ohms c. 44 ohms, 77 ohms22. Car: 25 mi/hr; Bicycle: 10 mi/hr

8-3 Part E

1. 7.6 2. − 79 3. 0.25 4. 3.75 5. (x−3)(2x−5)

(x+2)(x+4)

6. 1x+3 7. u(u+4)(u−7)

2(u−3) 8. 1(c−5)(c+4)

9. 7z2 −35z+21(z−5)(z−2) 10. − 12s+1

(s−5)(s+3)(2s+1)

11. x = –7, x = –2 12. x = –5, x = 3 13. x = –2, x = 514. x = 415. Asymptote at x = –1; Possible answer:

x –3 –2 0 1 2 3y 3

23 –3 − 3

2–1 − 3

4

y5

0 x5

16. “Hole” at x = 2; Possible answer:x –1 0 1 3 4 5y 1 0 1 9 16 25

y5

0 x5

17. x = –2 or x = 5 18. x = –2 or x = 7 19. x = –13

20. x = –22 or x = 7 21. x = − 277 or x = 5

22. x = –3 or x = 3

CHAPTER 9

9-1 Part A

1. 14 2. 1 3. 4 4. 1

256 5. 4t+4 6. 43v−1

7. 81 8. 9 9. 19

10. 127

11. 13( )4a+2

12. 13( )z−3

or 33−z

Answers



5

0 x5

(0, 1)

(2, )1 25


5

0 x5

(0, 1)

(1, 3)

15. x = 4 16. x = –5 17. x = –1 18. x = 12

19. x = − 43 20. x = 5

2 21. x = 43 22. x = –2

23. x = –3 24. x = − 32 25. a. P = 300, 000(1.075)t

b. About 618,309

9-1 Part B

1. 19,852 tons 2. 31,238 tons 3. 49,153 tons4. 121,701 tons 5. 377,986 tons 6. 2,068,932 tons7. a. 0.6% b. P = 1,273,854(1.006t ) c. 1,410,2158. a. 2.5% b. V = 178, 000(0.975t ) c. About$130,000 9. a. 2.8% b. R = 425(1.028t)c. About $680 10. In 2001 11. a. n = 800 1

2( )t / 48

b. 303.5 minutes or 5.06 hours

9-1 Part C

1. Exponential 2. Linear 3. Exponential 4. 0.6255. About 487.71 6. About 3.03 7. About 1586.878. a. 6% per year b. i. About $180,436 ii. About$241,464 iii. About $384,856 9. a. 1976 b. 1980c. 1984 d. 198710. y = 3.45(1.076)x

y100

80

60

40

20

0 10 20 30 40x

50

11. y = 10.18(0.978)x

y10

8

6

4

2

0 20 40 60 80x

100

9-1 Part D1. 8.24 years 2. 6.36% 3. 6.08 years 4. 3000;3169.62; 3538.18; 4172.9; 5199.76 5. 10,000; 7945.34;5015.76; 2515.79; 1002.59 6. 8; 9.77; 14.58; 26.56;59.11 7. 500; 475.61; 430.35; 370.41; 303.278. $2210.34 9. $6127.35 10. $1564.2611. $957.77

12. a. A = 700 ⋅ e0.1t

y2000

1000

0x

105Year

b. i. $1902.80ii. $1902.54iii. $1894.93iv. $1815.6213. a. 359,181b. 484,843 c. 11,894,426

9-1 Part E

1. 1000; 750; 562.50, 177.98, 56.31 2. 150; 163.50;178.22; 251.57; 355.10 3. 2000; 2081.62; 2166.57;2542.50; 2983.654. Possible answer:

y5

0 x5

(0, 1)9 4(2, )


5

0 x5

(0, 1)5 4(21, )

6. x = –3 7. x = 72 8. x = − 2

3 9. x = –410. 3 hours 11. a. $5310.43 b. $5405.29c. $5427.70 d. $5439.09 12. a. 4.5% per yearb. i. 9,311 ii. 15,110 iii. 31,934

9-2 Part A


5

0 x5

(2, 1)

(1, 0)


5

0 x5

(1, 0)

(3, 21)


5

0 x5

(1, 0)

( , 21)1 10


5

0 x5

(1, 1)(21, 0)

5. 25 = 32 6. 3−4 = 181 7. log6 36 = 2

8. 105 = 10, 000 9. log1/ 4 64 = −3 10. log5 125 = 3

11. –3 12. –3 13. 4 14. –2 15. 0.76 16. 6.33

17. x = 32 18. x = 19 19. x = √ 6 20. x = 1

2

21. x = 12 22.

1125

9-2 Part B1. x < 1.74 2. x < –1.30 3. x < 11.76 4. x < 5.115. x < 1.18 6. x < 6.77 7. t < 8.088. x = 2 or x = 3 9. x < 167.06 10. x < 24.41

11. x < 133.62 12. x < 3.38 13. a. A = 2000e0.08t

b. 11.45 years; No c. 5000 = 2000e10r ; 9.16%14. a. 6.24 years b. 10.66 years c. 16.90 yearsd. 35.42 years 15. a. 22.91% b. 10.18% c. 6.11%

d. 3.27% 16. a. P = 5000(10t ) b. t < 1.30

9-2 Part C1. False; log 4 + log 7 = log(4 ⋅ 7) 2. False;

log 35 = 5 log 3 3. True; Logarithm of a Quotient


4. False; eln 5 = 5 or 10log 5 = 5 5. log t5

6. log 2 7. ln x4

y5

8. log2b5

ac2( ) 9. log 8q2

p4

10. log x 2zy2

11. 4 log x + 8 log y

12. ln 3 + ln a + ln c 13. 2 log u − log v − log w14. ln 3 + ln a + ln b − 2 ln c

15. log5 4 + log5 a + log5(x + y) 16. 12 log x + 1

2 log y

17. x = 2 18. x < 2.40 19. x < 19.83 20. x = 121. x = 8 22. x < –1.82 23. x < 15.59 24. x = 625. 1.21 26. 5.75 27. –1.38 28. 2.45 29. 430. 0.48

9-2 Part D


5

0 x5

(1, 0)

(4, 22)


5

0 x5(23, 0)

(21, 1)

3. log4 8 = 32 4. log 1000 = 3 5. 35 = 243

6. 3612 = 6 7. 10−5 = 0.00001 8. log4/5

12564( ) = −3

9. 2.33 10. –3 11. –1.5 12. 4 13. 2.64 14. 5.02

15. a. 6.68 years b. 8.51% 16. log u2

v4( )17. log 12 18. log2 (ad) 19. log(x3y2 )

20. ln p2rs4

q

21. log(x – 5) 22. x = 32 23. x = 5

24. x < 0.71 25. x = 25 26. x < 4.26 27. x = 47.5

CHAPTER 10

10-1 Part A

1. 2129 2.

2029 3.

2021 4.

2129 5.

2921 6.

2021 7. 60

8. 79.68 9. 10.48 10. 24.9 11. 20.1 12. 398

m/A sin A cos A tan A csc A secA cot A13. 408 0.643 0.766 0.839 1.556 1.305 1.19214. 258 0.423 0.906 0.466 2.366 1.103 2.14515. 328 0.530 0.848 0.625 1.887 1.179 1.60016. 738 0.956 0.292 3.271 1.046 3.420 0.30617. m/A < 17.58 18. m/B < 45.68 19. m/C = 45820. m/D = 308 21. m/E < 66.48 22. m/F < 67.4823. a. 13 ft b. 7 ft 24. 20 ft

10-1 Part B

1. 7π36 2. 2π

5 3. 25π36 4. π

18 5. 7π90 6. 13π

60

7. π2 8. 2π 9. 458 10. 67.58 11. 1058

12. 608 13. 1808 14. 728 15. 548 16. 80817. 0.924 18. 0.975 19. 3.078 20. 0.96621. 0.822 22. 3.986 23. 0.999 24. 0.673

25. √ 2 26. √ 2 27. 3 28. 2 33

29. 400π < 1256.6 30. 5π6 < 2.62 31. 2970 mi

10-1 Part C

1. About 11.00 cm 2. About 28.27 in. 3. 6.9 m4. About 4.28 ft 5. About 2.18 cm 6. About 23.56 in.7. 5.85 m 8. About 8.64 ft 9. About 230.91 cm2

10. About 50.89 in.2 11. About 392.70 mm2

12. About 69.81 ft2 13. About 8.48 in.2 14. About30.54 m2 15. About 4.28 cm2 16. 10.16 ft2

17. About 380 mi 18. About 6442 mi19. About 709.04 mi2 20. About 4900.89 in./min21. About 48,738 radians/hr or 13.5 radians/sec22. About 6.28 in.2

10-1 Part D1. 1358; II 2. 2118; III 3. 1558; II 4. 3358; IV5. 458; I 6. 2888; IV 7. 2408; III 8. 3158; IV

9. –45;

35; –

43 10.

725;

2425;

724 11.

817; –

1517; –

815

12. –1161; –

6061;

1160 13.

817;

1517;

815 14. –

2129;

2029; –

2120

15. –513; –

1213;

512 16.

45; –

35; –

43 17. –

12 18. –

√ 32

19. –1 20. 2 21. 2√ 3

3 22. 0 23. 0 24. –2

25. a. θe (t) = 15t b. θs (t) = 36013 t c. At t < 28.36 hr

10-1 Part E

1. 15 2. 61.98 3. 28.18 4. About 6.1 ft 5. 5π12

6. a. 2π radians/min < 6.28 radians/min b. 6π m/hr <18.85 m/hr 7. About 90 mi 8. About 38.48 in.2

9. a. About 74.70 rev/min b. About 469.33 radians/min

10. − 22 11. – 3

3 12. –√ 2 13. –1 14. m/A

< 84.38 15. m/B < 53.18 16. m/C < 35.0817. m/D < 56.38

10-2 Part A

1. 10.4 2. 31.4 3. 35.2 4. 129.1 5. 256. 39.4 7. 14.0 8. 51.58 9. 29.98 10. 28.7811. 608 12. 32.28 13. 908 14. 84.9815. About 23.7 cm; About 49.9 cm 16. a. 300 mi/hrb. About 354 mi/hr c. About 394 mi/hrd. About 384 mi/hr 17. About 55.6 mi18. About 64.28; About 43.58; About 72.48

10-2 Part B

1. 7.9 2. 3.2 3. 89.8 4. 17.1 5. 63.9 6. 3.87. 424.2 8. 109.8 9. 141.8 10. 389.7 11. 33.812. 1184.7

Answers


m/A m/B m/C a b cArea

nABC13. 578 388 858 31.3 23 37.2 358.914. 258 838 728 14 32.9 31.5 218.915. 498 24.58 106.58 29.1 16 37 223.416. 278 1108 438 18 37.3 27.0 228.717. 89.58 32.08 58.58 34 18 29 261.018. 39.38 106.78 348 43 65 37.9 781.519. 13.80 m2 20. About 71.4 m

10-2 Part C

1. 49.7 2. 26.0 3. 29.9 4. 39.5 5. 33.8 6. 507. 26.58 8. 62.78 9. 107.58 10. 41.48

m/A m/B m/C a b cArea

nABC11. 44.88 74.68 60.68 38 52 47 860.912. 44.78 94.38 418 12 17 11.2 66.913. 498 818 508 22.7 29.7 23 257.414. 538 758 528 28.9 35 28.6 399.115. About 41.7 in.; About 16.2 in. b. About 288.1 in.2

16. a. About 73.08 b. About 67,995 ft2

17. About 136.7 lb

10-3 Part A

1. About 5.0; 4 2. About 5; 2π3. 1; 2π

3y

5

x2p0

4. 3; πy

5

0x

2p

5. y = 4 sin x 6. y = 3 sin 0.4x 7. y = 1.7sin 2πx3

8. y = 0.3sin 2πx 9. y = 2 sin 8x 10. y = 0.75 sin 5x

10-3 Part B

1. a. –1 b. 2 c. π2. 2; 2π

3 ; 0; π3

y5

0x

2p

3. 1; 2π ; –3; π2

y5

0x

2p

4. y = sin x − π2( ) + 3 5. y = 3sin 2

3 (x − π)

6. y = 5sin 4π3 (x − 1) − 2 7. y = 0.25sin 4x + 1.8

8. y = 2.3sin 2π7 (x − 3) + 3.7

9. y = 1.5sin 52 x − π

5( ) − 5.5

10-3 Part C

1. 32 ; 2π; 1

2 ; − π2

y5

0x

2p

2. 2; 3π; − 2; 3π4

y5

0x

2p


5

0x

5

4. y = 4sin 6 x − π12( ) + 10

5. y = 3sin 2 x − π5( ) − 2

6. y = 2.5sin 2π5 (x − 3)

7. y = sin 23 (x − π)+ 4

8. y = 1.7sin 2πx + 2.5 9. y = 0.6sin x − π4( ) + 1

CHAPTER 11

11-1 Part A

1. 19 < 0.11 2.

29 < 0.22 3.

79 < 0.78 4.

59 < 0.56

5. 23 < 0.67 6. 0.02 7. 0.04 8. 0.49 9. 0.17

10. 0.06 11. 0.76 12. 0.25 13. 0.75 14. 0.64315. 0.75 16. 0.464 17. 0.35 18. a. 15,504

b. 816 c. 17323 < 0.053 d.

306323 < 0.947

11-1 Part B1. Dependent, colleges base admission decisions in part ongrades. 2. Dependent, a traffic accident can make onelate to an appointment. 3. Independent, the deck ofcards and the coin do not affect one another. 4. 0.05585. 0.2015 6. 0.117 7. 0.03627 8. 27% 9. 0.15

10. a. 1216

< 0.0046 b. 136

< 0.0278

c. 3536( )5

< 0.8686 11. a. 95% b. 90% c. 85.5%

d. 14.5%

11-1 Part C1. a. Dependent b. Sampling without replacement2. a. Independent b. Neither 3. a. Independent

b. Sampling with replacement 4. 299 < 0.02

5. 133 < 0.03 6.

199 < 0.01 7. 0 8.

111 < 0.09

9. 199 < 0.01 10.

2551 < 0.49 11.

451 < 0.08

12. 117 < 0.06 13.

1351 < 0.25 14.

417 < 0.24

15. 1351 < 0.25 16. 82.68% 17. 3.5% 18. a.

12 = 0.5

b. 18 = 0.125 c.

14 = 0.25


11-1 Part D

1. Independent, the events do not affect one another.2. Dependent, sunny weather today means sunny weathertomorrow is more likely. 3. Dependent, winning thelottery usually means a person will have money.4. 0.12 5. 0.06 6. 0.83 7. 0.14 8. 0.019. 0.01 10. 0.16 11. 12%

11-2 Part A

1. Possible answer: Children; Sample; it is impractical tointerview all children. 2. Possible answer: Books;Sample; All copies of the same book will have the sametypes, so it is only necessary to proofread one copy of eachbook. 3. Possible answer: Students in the class; Entirepopulation; Each student must be tested in order to receivea grade.4. 25%

20%

15%

10%

5%

1 2 3 4 5 6 7 8 9

5. 4806. Possible answer:Students in a calculusclass may not berepresentative of theentire student body.

7. Possible answer: The people on a politicalorganization’s mailing list are more likely to agree withthat organization’s point of view. 8. Possible answer: Ifthe restaurant staff knows that a patron will be writing areview of her meal, they may be inclined to give herspecial treatment.

11-2 Part B

1. 70; 80 2. 65; 85 3. 65 4. 85 5. 34%6. 47.7% 7. 68% 8. 2.3% 9. Good model, heightsare usually normally distributed. 10. Good model,expect a normal distribution with average around 15 years.11. Good model, expect a normal distribution with averagearound 40 hours 12. Poor model, the coins only take onvalues of 1¢, 5¢, 10¢, 25¢, 50¢ and $1, so a normaldistribution is impossible. 13. About 16%; 2.3% will bebelow 1.9 oz and 13.6% will be between 1.9 oz and 2 oz,so we add these figures. 14. a. About 0.023b. About 0.16 c. About 0.50 d. About 0.136

11-2 Part C

1. Possible answer: The film; Sample; The film cannot beused after it has been tested. 2. Possible answer:Americans; Sample; It would be impractical to measureevery American’s water intake.3. 20%

16%

12%

8%

4%

2 4 6 8 10 121416 18 20

4. Possible answer:Teachers in affluentareas may not beknowledgeable aboutsituations in other areas.5. About 1,143,000voters

6. 55; 71 7. 47; 79 8. 47 9. 7910. a. About 0.68 b. About 0.136c. About 0.477 d. About 0.023

CHAPTER 12

12-1 Part A

1. 7 faces, 8 vertices, 13 edges; 7 + 8 – 13 = 2√2. 5 faces, 6 vertices, 9 edges; 5 + 6 – 9 = 2√3. 12 4. 7 5. a. 20 b. 30 c. 126. Possible answer:

A

B

C

D

E

F7. a. 6 b. 98. Yes; Possible answer:

U1 U2

12-1 Part B

1. Not connected 2. Connected 3. This is an Eulerpath because every edge is traversed exactly once. 4.This is not an Euler path because #2 and #6 traverse thesame edge. 5. A: 5; B: 5; C: 5; D: 5; E: 4; F: 3; G: 4;H: 3; I: 4; J: 3; K: 4; L: 3; No Euler circuit or path.6. A: 3; B: 2; C: 2; D: 3; E: 2; F: 2; Euler path (possibleanswer): ABCADEFD7. Possible answer:ABCDEFAECFBDA

A B

CD

E F

8. No, each edge connectstwo vertices, so the sum ofthe degrees is twice thenumber of edges. Since thesum of the degrees is aneven number, it isimpossible for exactly onevertex to have an odddegree.

12-1 Part C

1. Possible answer: ABCDHGEFA 2. Possible answer:ABCDIEHGFA 3. Yes, it is connected and contains nocircuits. 4. No, it is not connected.5. A B C D

E F G

H I

6. A B

DE

FG

HC

7.

G

EF

CB

A D

8.G HE F

CBA D

KJI L

9. Possible answer:ABCDEJIHGFA

A

BE

CD

I HGJ

F

10. ABDCA or ACDBA

Answers


12-1 Part D1. Possible answer:

FG

K H I

L J

2. Possible answer:BCDEFGABDIFHIGHB;Possible answer:ABCDEFIHGA

3. $2600

T W

U V

Y X

Z

4. 17 5. Euler path,exactly two vertices haveodd degree. 6. Neither,more than two verticeshave odd degree.7. Yes, it is connected andhas no circuits. 8. No,it is not connected.

12-2 Part A1. 100, 60, 40, 30, 25, 22.5,21.25, 20.625

an100

80

60

40

20

0 2 4 6 8n

10

2. 2, –2, 4, –5, 8.5, –11.75,18.625, –26.9375

an25

0 n10

3. an = −3 + 92 (2n ); a10 = 4605; Does not converge

4. an = 92 + 459

213( )n

; a10 = 98502187 < 4.50; Converges

5. an = 32 − 3

2 (−1)n ; a10 = 0; Does not converge

6. an = − 43 − 17

3 (−2)n ; a10 = −5804; Does not converge

7. an = − 59 + 7

45 (10n ); a10 = 1,555,555,555; Does not

converge 8. an = 203 − 80

3 − 12( )n

; a10 = 42564 < 6.64;

Converges 9. a1 = 600 and an = 1.08an−1 + 400; 20

years 10. an = 2000 + 80,00011 (1.1)n (does not

converge); an = 2000 (converges)

12-2 Part B1. No, the columns do not add to 1. 2. No, –0.1 is not aprobability. 3. No, the entries are not probabilities andthe columns do not add to 1. 4. No, the matrix is notsquare. 5. 0.5; 0.8 6. 0.77; 0.09 7. 0.7; 0.3

8. 0.872; 0.105 9. A2 =0.37 0.36

0.63 0.64

;

A3 =0.363 0.364

0.637 0.636

;

L =4

114

117

117

11

≈0.3636 0.3636

0.6364 0.6364

10. B2 =.68 .32

.32 .68

; B3 =0.392 0.608

0.608 0.392

;

L =12

12

12

12

=0.5 0.5

0.5 0.5

11. C2 =0.775 0.525

0.225 0.475

;

C3 =0.7375 0.6125

0.2625 0.3875

; L =

710

710

310

310

=0.7 0.7

0.3 0.3

12. D2 =0.6788 0.6059

0.3212 0.3941

; D3 ≈0.647 0.666

0.353 0.334

L ≈83

12783

12744

12744

127

≈0.6535 0.6535

0.3465 0.3465

13. a. .75 .45

.25 .55

b. 450; 585; About 626; About 643

12-2 Part C1. 5, 6, 8, 12, 20, 36, 68,132

an100

80

60

40

20

0 2 4 6 8n

10

2. 10, 3, –0.5, –2.25,–3.125, –3.5625, –3.78125,–3.890625

an10

0n

10

3. an = −10 + 143 (3n ); a10 = 275,552; Does not converge

4. an = 1.25 + 493.75(0.2n ); a10 < 1.25; Converges

5. an = 503 − 5900

3 (−0.5)n ; a10 < 14.75; Converges

6. A2 =0.28 0.24

0.72 0.76

; A3 =0.244 0.252

0.756 0.748

;

L =0.25 0.25

0.75 0.75

7. B2 =0.72 0.56

0.28 0.44

;

B3 =0.688 0.624

0.312 0.376

; L =23

23

13

13

≈0.6667 0.6667

0.3333 0.3333

8. $4850; $4722.50; $4000 + 1176.47(0.85)n 9. a.0.9 0.15

0.1 0.85

b. 525,000; 543,750; 600,000

1-1a practice - miller...

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