student handbook - menifee county › userfiles › 27 › classes › 343 › student...

802

StudentHandbook

692

Student Handbook 693

Student

Handbook

Built-In Workbooks

Prerequisite Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694

Extra Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717

Mixed Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . 744

Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . 756

Reference

English-Spanish Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . R2

Selected Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R20

Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R61

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R63

Formulas and Symbols. . . . . . . . . . . . . . Inside Back Cover

What if I Forget What I Learned Last Year?

Use the Prerequisite Skills section to refresh

your memory about things you have learned in

other math classes. Here’s a list of the topics

covered in your book.

1. Operations with Fractions: Adding and

Subtracting

2. Adding and Subtracting Rational Numbers

3. Operations with Fractions: Multiplying and

Dividing

4. Multiplying and Dividing Rational Numbers

5. The Percent Proportion

6. Perimeter and Area of Squares and

Rectangles

7. Area and Circumference of Circles

8. Volume

9. Probability: Simple Probability and Odds

10. Mean, Median, and Mode

11. Box-and-Whisker Plots

12. Representing Data

13. Absolute Value

What If I Need More Practice?

You, or your teacher, may decide that working

through some additional problems would be

helpful. The Extra Practice section provides these

problems for each lesson so you have ample

opportunity to practice new skills.

What If I Have Trouble with Word Problems?

The Mixed Problem Solving portion of the book

provides additional word problems that use the

skills presented in each lesson. These problems

give you real-world situations where math can

be applied.

What If I Need Help on Taking Tests?

The Preparing for Standardized Tests section

gives you tips and practice on how to answer

different types of questions that appear on tests.

What If I Forget a Vocabulary Word?

The English-Spanish Glossary provides a list of

important or difficult words used throughout the

textbook. It provides a definition in English and

Spanish as well as the page number(s) where the

word can be found.

What If I Need to Check a Homework Answer?

The answers to odd-numbered problems are

included in Selected Answers. Check your

answers to make sure you understand how to

solve all of the assigned problems.

What If I Need to Find Something Quickly?

The Index alphabetically lists the subjects

covered throughout the entire textbook and the

pages on which each subject can be found.

What if I Forget a Formula?

Inside the back cover of your math book is a list

of Formulas and Symbols that are used in the

book.

The Student Handbook is the additional skill and reference material found at the

end of the text. This Handbook can help you answer these questions.How to Use the

Student Handbook

692

Student Handbook

693

Use the Prerequisite

Skills se

ction to

refre

sh

your memory about th

ings you have le

arned in

other math classe

s. Here’s a

list o

f the to

pics

covered in your b

ook.

Operations w

ith Fractio

ns: Adding and

Subtractin

g

Adding and Subtractin

g Rational N

umbers

Operations w

ith Fractio

ns: Multip

lying and

Dividing

Multiplying and D

ividing Rational N

umbers

The Percent Proportio

n

Perimeter a

nd Area of Squares a

nd

Rectangles

Area and Circumference of C

ircles

Volume

Probability: S

imple Probabilit

y and Odds

Mean, Median, and M

ode

Box-and-Whisk

er Plots

Representing D

ata

Absolute Value

You, or y

our teacher, m

ay decide that w

orking

through some additio

nal problems w

ould be

helpful. The Extra

Practice se

ction provides th

ese

problems for e

ach lesso

n so you have ample

opportunity

to practic

e new skills

.

The Mixed Problem Solving portion of th

e book

provides additio

nal word problems th

at use th

e

skills presented in

each lesso

n. These problems

give you real-w

orld sit

uations w

here math can

be applied.

The Preparing fo

r Standardized Tests se

ction

gives you tip

s and practic

e on how to answ

er

different ty

pes of q

uestions th

at appear o

n tests

.

The English-Spanish G

lossary provides a lis

t of

importa

nt or d

ifficult w

ords used th

roughout the

textbook. It provides a

definitio

n in English

and

Spanish as w

ell as th

e page number(s) w

here the

word can be found.

The answers

to odd-numbered problems are

included in Selected A

nswers. Check your

answers

to make su

re you understand how to

solve all of th

e assigned problems.

The Index alphabetically

lists t

he subjects

covered throughout th

e entire te

xtbook and the

pages on w

hich each subject can be fo

und.

Inside th

e back cover of y

our math book is

a list

of Formulas and Symbols th

at are used in

the

book.

The Student Handbook is

the additional sk

ill and re

ference materia

l found at th

e

end of the te

xt. This H

andbook can help you answer th

ese questions.

692


Use the Prerequisite Skills section to refresh

your memory about things you have learned in

other math classes. Here’s a lis

t of the topics

covered in your book.

Operations with Fractions: Adding and

Subtracting

Adding and Subtracting Rational Numbers

Operations with Fractions: Multiplying and

Dividing

Multiplying and Dividing Rational Numbers

The Percent Proportion

Perimeter and Area of Squares and

Rectangles

Area and Circumference of Circles

Volume

Probability: Simple Probability and Odds

Mean, Median, and Mode

Box-and-Whisker Plots

Representing Data

Absolute Value

You, or your teacher, may decide that working

through some additional problems would be

helpful. The Extra Practice section provides these

problems for each lesson so you have ample

opportunity to practice new skills.

The Mixed Problem Solving portion of the book

provides additional word problems that use the

skills presented in each lesson. These problems

give you real-world situations where math can

be applied.

The Preparing for Standardized Tests section

gives you tips and practice on how to answer

different types of questions that appear on tests.

The English-Spanish Glossary provides a list of

important or difficult words used throughout the

textbook. It provides a definition in English and

Spanish as well as the page number(s) where the

word can be found.

The answers to odd-numbered problems are

included in Selected Answers. Check your

answers to make sure you understand how to

solve all of the assigned problems.

The Index alphabetically lists the subjects

covered throughout the entire textbook and the

pages on which each subject can be found.

Inside the back cover of your math book is a list

of Formulas and Symbols that are used in the

book.

The Student Handbook is the additional skill and reference material found at the

end of the text. This Handbook can help you answer these questions.

69 2

Student Handbook 693Use the Prerequisite Ski lls sec tionto refre shyour memoryabout th ings youhave lear ned ino ther ma th clas ses .He re’s alist of the topicscove red in your book .Ope rations with Fra ctions: AddingandSubtr actingAdding andSubtra cting Rat ional Numbe rsO pe ratio ns w ith Fr actions :MultiplyingandDiv idi ngMultiply ingand DividingRational N umbersThe Perc entProportio nPerimete rand Are a of Square s andRectang lesAre a andC irc um fere nc e of Circle sVo lumeProbability :S imple Probability andO ddsMean ,Median,and ModeBox- and-Wh isker Plo tsRe pre sen ting DataAbsolute ValueYou, or yourte acher, may dec ide that workingth roughsome additional problems wouldbehe lpful.The Extra Pra ctice se ction pr ovides the seproblems for e ach le ssonso youhave ampleopportunity toprac tic e new sk ills.TheMixed Pro blemSo lving por tiono f the bookprov ides addi tional wordproblems that us e theskills prese nte dine ach lesson.The se problemsgive you real-w or ld situations where math canbe applied.

The Prepari ng fo r Standard izedTests se ctiongive s youtips andprac tice onhow to answe rdiffe renttypes o fquestions that appea ronte sts.The En glis h-Spanish Glossary provides a list ofimportant or di ffic ult words us ed throughout thetex tbook. It provide s a definition inEn glish andS pan is hasw ellas the page number(s )whe re thewo rdcan be found.The ans wers to odd-numbe redproble ms ar einclude dinSelec ted Answers .Check youranswers tomake sure youunde rstand how toso lve al lo fthe as signed prob lem s.The Index alphabe tically lists the subjec tsc overe dthroughoutthe e ntire tex tbookandthepages onwhiche ach sub je ctcan be found.Inside the back cove r of your math book is a lis to f Formula s andSy mbols that ar e used in thebook.The Stude nt H andbook is th e addi tional sk ill andre fere nc e material founda tthe

e nd o fthe text. This H andbook can he lpyou answe r the se que stions.

Built-In WorkbooksProblem-Solving Handbook. . . . . . . . . . . . . . . . . . . . . . . 804

Extra Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815

Mixed Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . 845

Concepts and Skills Bank. . . . . . . . . . . . . . . . . . . . . . . . . 857

ReferenceKey Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1

Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . R12

Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R94

Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R96

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R120

Formulas and Measures. . . . . . . . . . . . . Inside Back Cover

Symbols and Properties . . . . . . . . . . . . . Inside Back Cover


What If I Need Problem-Solving Practice?You have probably used several different problem-solving strategies in previous math courses. The Problem-Solving Handbook section provides example and problems for refreshing your skills at using various strategies.

What If I Need More Practice?You, or your teacher, may decide that working through some additional problems would be helpful. The Extra Practice section provides these problems for each lesson so you have ample opportunity to practice new skills.

What If I Have Trouble with Word Problems?The Mixed Problem Solving portion of the book provides additional word problems that use the skills presented in each lesson. These problems give you real-world situations where math can be applied.

What if I Forget What I Learned Last Year?Use the Concepts and Skills Bank section to refresh your memory about things you have learned in other math classes. Here’s a list of the topics covered in your book.

1. Converting Units of Measure 2. Factors and Multiples 3. Prime Factorization 4. Measuring Angles 5. Venn Diagrams 6. Misleading Graphs

What If I Need to Check a Homework Answer?The answers to odd-numbered problems are included in Selected Answers and Solutions. Check your answers to make sure you understand how to solve all of the assigned problems.

What If I Forget a Vocabulary Word?The English-Spanish Glossary provides a list of important or difficult words used throughout the textbook. It provides a definition in English and Spanish as well as the page number(s) where the word can be found.

What If I Need to Find Something Quickly?The Index alphabetically lists the subjects covered throughout the entire textbook and the pages on which each subject can be found.

What if I Forget a Formula?Inside the back cover of your math book is a list of Formulas and Symbols that are used in the book.

The Student Handbook is the additional skill and reference material found at the end of the text. This Handbook can help you answer these questions.

How to Use the

Student Handbook

Prob

lem

-Sol

ving

Han

dboo

k

804 Problem-Solving Handbook

Problem-Solving Handbook

Problem-Solving Strategy: Look for a PatternThere are many problem-solving strategies in mathematics. One of the most common is to look for a pattern. To use this strategy, analyze the first few numbers or figures in a pattern and identify a rule that relates the first number or figure in the pattern to the second, and then to the third, and so on. Then use the rule to extend the pattern and find a solution.

EXAMPLE

Refer to the graph. Describe the pattern in the y

x

coordinates and predict the next point in the pattern in the positive direction.

Step 1 List the coordinates of the points shown on the graph.

(-3, -5), (-2, -3), (-1, -1), (0, 1), (1, 3), and (2, 5)

Step 2 Identify the pattern in the x-coordinates and the y-coordinates.

As the x-coordinates increase by 1, the y-coordinates increase by 2 each time. So in the positive direction, the next point is (2 + 1, 5 + 2) or (3, 7).

Practice

Solve each problem by looking for a pattern.

1. The graph of a function passes through the points

y

x

shown.

a. Describe the pattern in the coordinates, and predict the next point in the pattern in the positive direction.

b. Predict the next point in the pattern in the negative direction.

2. List the first five common multiples of 3, 4, and 6. Write an expression to describe

all common multiples of 3, 4, and 6.

3. What is the perimeter of the twelfth figure? Figure 1

Perimeter – 6Figure 2

Perimeter – 8Figure 3

Perimeter – 10

4. The football parent booster group sold hot Number of Cups Sold

Amount of Money Raised ($)

15 11.25

30 22.50

45 33.75

60 45.00

75 ?

chocolate at the game on Friday night. The table shows the total amount of money raised based on the number of cups of hot chocolate sold. Use this data table to determine how much money would be raised selling 75 cups of hot chocolate.


Problem-Solving Handbook 805

Problem-Solving Strategy: Create a TableOne strategy for solving problems is to create a table. A table allows you to organize information in an understandable way.

EXAMPLE

A fruit machine accepts dollars, and each piece of fruit costs 65 cents. If the machine gives only nickels, dimes, and quarters, what combinations of those coins are possible as change for a dollar?

The machine will give back $1.00 - $0.65 or Quarters Dimes Nickels

1 1 0

1 0 2

0 3 1

0 2 3

0 1 5

0 0 7

35 cents in change in a combination of nickels, dimes, and quarters.

Make a table showing different combinations of nickels, dimes, and quarters that total 35 cents. Organize the table by starting with the combinations that include the most quarters.

The total for each combination of the coins is 35 cents. There are 6 combinations possible.

Practice

Solve each problem by creating a table.

1. How many ways can you make change for a half-dollar using only nickels, dimes, and quarters?

2. A penny, a nickel, a dime, and a quarter are in a purse. How many amounts of money are possible if you grab two coins at random?

3. How many ways can you receive change for a quarter if at least one coin is a dime?

4. Johanna had a bag of four marbles. One marble is blue. Two marbles are green. One marble is orange. How many different ways are there to draw the marbles out of the bag one at a time?

5. At Midas High School, students are selling popcorn at a football game. Each small bag of popcorn is $1.25. Each large bag of popcorn is $2.25. Create a table to show the purchase price of up to five bags of each size of popcorn.

6. Make a table to show the ordered pairs that satisfy the equation f(x) = 3 x 3 - 4. Use the domain of integers between 3 and 10.

7. The equation of a line is y = 1 _ 2 x - 2. Create a table to show five ordered pairs

with x-coordinates belonging to the set {-2, -1, 0, 1, 2}.

8. Aria asked her friends whether they used wrapping paper, gift bags, recycled paper, or no wrapping to wrap birthday presents. Create a table to show how many students preferred each method of the24 students she asked. Then predict how many would choose each method if 120 students were asked.

Prob

lem

-Sol

ving

Han

dboo

k


Problem-Solving Strategy: Make a ChartData presented in a problem can be organized by making a chart. This problem-solving strategy allows you to see patterns and relationships among data.

EXAMPLE

Find the time needed to stop each car using the data given in the diagram.

Auto stopping distanceSpeed (mph)

55

Distance (feet)

65

75

273

355

447

Source: AAA Foundation for Traffic Safety

Step 1 Make a chart that includes the information given, the speed and the distance, and leave a column for the information needed to answer the question, time. Before setting up your chart, think about how speed, distance, and time are related. Include rows for Car 1, Car 2, and Car 3.

The distance formula is distance = rate of speed × time. So, use distance, rate, and time as three columns in your chart. Fill in the information given in the diagram.

Car Distance (ft) Rate of Speed (mph) Time

1 273 55

2 355 65

3 447 75

Step 2 Since the distance is listed in feet, find the rate of speed it takes to stop in feet per second. To convert from miles per hour to feet per second, multiply by a conversion factor of 3600 s/5280 mi.

Car Distance (ft) Rate of Speed (ft/s) Time

1 273 37.5

2 355 44.3

3 447 51.1

Step 3 To find the time needed to stop, divide each distance by each rate of speed. Time will be in seconds.

Car Distance (ft) Rate of Speed (ft/s) Time (s)

1 273 37.5 7.28

2 355 44.3 8.01

3 447 51.1 8.75

So, the time needed to stop would be about 7.28 seconds at 55 mph, 8.01 seconds at 65 mph, and 8.75 seconds at 75 mph.



Practice

Solve each problem by making a chart.

1. As the length of a square doubles, 3 cm 6 cm 12 cmthe area increases by a scale factor. Using the squares in the diagram, make a chart of each length and each area. Then find the scale factor.

2. Given the functions f(x) = 2x + 3 and g(x) = -x - 3, use a table to find f(x) - g(x) for all positive integers less than or equal to 6.

3. The chart shows at which When we seek gasStart looking when the fuel gauge reads

50%Quarter tank

Source: Bruskin/Goldring for Exxon

Half a tank

Less than a Quarter tank

2%Empty 14%

34%

point drivers determine when they are going to fill the gas tank. Make a chart to show how many people of 200 surveyed would be expected to have each response.

4. The following table shows the official state reptile in each state. Make a tally chart that shows how many states have turtles (tortoise, terrapin), snakes, alligators, lizards, toads, or none. Find the ratio of states with alligators to states with no official state reptile.

AL red-bellied turtle LA American alligator OH black racer (snake)

AK none ME none OK collared lizard

AZ ridge-nosed rattlesnake MD diamondback terrapin OR none

AR none MA garter snake PA none

CA desert tortoise MI painted turtle RI none

CO none MN Blanding’s turtle SC loggerhead turtle

CT none MS American alligator SD none

DE none MO three-toed turtle TN eastern box turtle

FL American alligator MT none TX Texas horned lizard

GA gopher tortoise NE none UT none

HI none NV desert tortoise VT none

ID none NH none VA none

IL painted turtle NJ none WA none

IN none NM whiptail lizard WV none

IA none NY snapping turtle WI none

KS ornate box turtle NC eastern box turtle WY horned toad

KY none ND none

Prob

lem

-Sol

ving

Han

dboo

k


Problem-Solving Strategy: Guess-and-CheckTo solve some problems, you can make a reasonable guess and then check it in the problem. You can then use the results to improve your guess until you find the solution. This strategy is called guess-and-check.

EXAMPLE

The product of two even consecutive integers is close to 1000.

Make a guess. Let’s try 24 and 26.

Adjust the guess upward.Try 30 and 32.

Adjust the guess upward again.Try 34 and 36.

Try between 30 and 34.Try 32 and 34.

The integers are 32 and 34.

This is the correct product.32 × 34 = 1088

30 × 32 = 960

34 × 36 = 1224 This product is too high.

This product is still too low.

24 × 26 = 624 This product is too low.

Practice

Solve each problem by using the guess-and-check strategy.

1. The product of two consecutive odd integers is 783. What are the integers?

2. Brianne is three times as old as Camila. Four years from now she will be just two times as old as Camila. How old are Brianne and Camila now?

3. Rafael is burning a CD for Selma. The CD will hold 35 minutes of music. Which songs should he select from the list to record the maximum time on the CD without going over?

Song A B C D E F G H I J

Time5 min

4 s9 min 10 s

4 min 12 s

3 min 9 s

3 min 44 s

4 min 30 s

5 min 0 s

7 min 21 s

4 min 33 s

5 min 58 s

4. Each hand in the human body has 27 bones. There are 6 more bones in the fingers than in the wrist. There are 3 fewer bones in the palm than in the wrist. How many bones are in each part of the hand?

5. The Science Club sold candy bars and soft pretzels to raise money for an animal shelter. They raised a total of $62.75. They made 25¢ profit on each candy bar and 30¢ profit on each pretzel sold. How many of each did they sell?

6. The product of two consecutive even integers is 4224. Find the integers.

7. Odell has the same number of quarters, dimes, and nickels. In all he has $4 in change. How many of each coin does he have?

8. Anita sold tickets to the school musical. She had 2 types of bills worth $75 for the tickets she sold. If all the money that the club collected was in $5 bills, $10 bills, and $20 bills, how many of each bill did Anita have?

9. Two angles of a triangle are shown. Find the third 38°32°angle if the three angles have a sum of 180°.



Problem-Solving Strategy: Work BackwardOn most problems, a set of conditions or facts is given and an end result must be found. However some problems start with the result and ask for something that happened earlier. The strategy of working backward can be used to solve problems like this. To use this strategy, start with the end result and undo each step.

EXAMPLE

Kendrick spent half of the money he had this morning on lunch. After lunch, he loaned his friend a dollar. Now he has $1.50. How much money did Kendrick start with?

Start with end result, $1.50, and work backward to find the amount Kendrick started with.

Kendrick now has $1.50.Undo the $1 he loaned to his friend.

Undo the half he spent for lunch.

The amount Kendrick started with was $5.00.

CHECK Kendrick started with $5.00. If he spent half of that, or $2.50, on lunch and loaned his friend $1.00, he would have $1.50 left. This matches the amount stated in the problem, so the solution is correct.

$1.50 ______ + 1.00

$2.50 ______ × 2

$5.00

Multiply by 2 to undo spending half the original amount.

Add $1.00 to undo giving his friend $1.00.

Practice

Solve each problem by working backward.

1. A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 4. What is the number?

2. A certain bacteria doubles its population every 2 hours. After 3 full days, there are 600 bacteria in a culture. How many bacteria were there at the beginning of the first day?

3. To catch a 7:30 a.m. bus, Don needs 30 minutes to get dressed, 30 minutes for breakfast, and 5 minutes to walk to the bus stop. What time should he wake up?

4. Find the length of the side of the quadrilateral if 28 m

15 m

22 m

the perimeter is 83 meters.

5. Troy lives 1 1 _ 8 miles from his school. If he has

walked 1 _ 4 mile to meet a friend and then they

walked another 1 _ 2 mile to meet another friend,

how far do they still need to walk to get to school?

6. If a lizard in its cage weighs 23 pounds, find the weight of the lizard if the cage weighs 19 pounds and the sand weighs 2 pounds.

7. Mattie spent $125.50 on three items at the mall. She bought one pair of socks for $1.20, one pair of shoes for $48.95. How much money did she spend on the jacket she purchased?

Prob

lem

-Sol

ving

Han

dboo

k


Problem-Solving Strategy: Solve a Simpler ProblemOne of the strategies you can use to solve a problem is to solve a simpler problem. To use this strategy, first solve a simpler or more familiar case of the problem. Then use the same concept and relationships to solve the original problem.

EXAMPLE

Find the sum of the number 1 through 500.

Consider a simpler problem. Find the sum of the numbers 1 through 10. Notice that you can group the addends into partial sums as shown below.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

11

11

11

11

11

The number of sums is 5, or half the number of addends.

Each partial sum is 11, the sum of the first and last numbers.

The sum is 5 × 11 or 55.

Use the same concepts to find the sum of the numbers 1 through 500.1 + 2 + 3 + … + 499 + 500 = 250 × 501

= 125,250

Practice

Solve each problem by solving a simpler problem.

1. Find the number of squares of any size in the game board shown at the right.

2. Find the sum of the numbers through 1000.

3. How many links are needed to join 30 pieces of chain into one long chain?

4. Three people can pick six baskets of apples in one hour. How many baskets of apples can 2 people pick in one-half hour?

5. A shirt shop has 112 orders for T-shirt designs. Three designers can make 2 shirts in 2 hours. How many designers are needed to complete the orders in 8 hours?

6. Find the area of the figure at the right. 7 cm

5 cm

3 cm

3 cm

6 cm

7. To add 3 _ 8 and 7 _

12 , how could you solve a simpler

problem that leads to the answer?

8. If one fourth of the 136 freshmen at Bayridge High School packed their lunches, explain how to use a simpler problem to find the number of students.

9. Explain how to find the greatest common factor of 35 and 49 using a simpler problem.

Multiply half the number of addends, 250, by the sum of the first and last numbers, 501.Multiply half the number of addends, 250, by the sum of the first and last numbers, 501.



Problem-Solving Strategy: Draw a DiagramAnother strategy for solving problems is to draw a diagram. There will be times when a sketch or diagram will give you a better picture of how to tackle a mathematics problem. Adding details like units, labels, and numbers to the drawing or sketch can help you make decisions on how to solve the problem.

EXAMPLE

Imani is trying to determine the number of 9-inch tiles needed to cover her patio. The rectangular patio measures 8-feet by 10-feet. What is the minimum number of 9-inch tiles Imani should purchase?

First, draw a diagram of the situation. Express the measurement of the patio in inches.

If each tile is 9 inches square, the

8 ft = 96 in.

10 ft = 100 in.

Patio

minimum number of tiles for the width of the patio is 96 ÷ 9 ≈ 10.7 or 11 tiles.

The minimum number of tiles for the length of the patio is 120 ÷ 9 ≈ 13.3 or 14 tiles.

So the minimum number of tiles Imani needs to cover the patio is 11 × 14 or 154 tiles.

Practice

Solve each problem by drawing a diagram.

1. The area of a rectangular flower bed is 24 square feet. If the sides are whole number dimensions, how many combinations of lengths and widths are possible for the flower bed? List them.

2. Kevin was hired to paint a mural on a wall that measures 5 feet by 20 feet. Starting from the center of the wall, he will paint a square that measures 3 feet. The dimensions of the next square will be 0.5 times greater than and centered on the previous square. How many squares can Kevin paint on the wall?

3. It takes 42 minutes to cut a 2-inch by 4-inch piece of wood into 7 equally sized pieces. How long will it take to cut a similar 2-inch by 4-inch piece into 4 equally sized pieces?

4. Find the number of line segments that can be drawn between any two vertices of an octagon.

5. How many different teams of 3 players can be chosen from 8 players?

6. A right triangle has measures of 11, 60, and 6111

60

61 millimeters. Find the area of the triangle.

7. Nitarren is trying to decide how many 9 inch diameter pies will fit on her dessert table that measures 4 feet by 2 feet. How many pies could Nitarren fit on the table?

Prob

lem

-Sol

ving

Han

dboo

k


Problem-Solving Strategy: Use EstimationWhen you need to make a decision on the basis of inexact information, a common strategy is to use estimation. Often estimation is used when an exact answer is not required or when mental math is used rather than a calculator or paper and pencil. You should use estimation to determine if your answer is reasonable.

EXAMPLE

In a recent year, 51 million international visitors came to the United States. Given the information in the table, estimate what percentage of the visitors were from Japan.

Step 1 Determine about how many international visitors came to the United States.

51 million or 51,000,000 would be an easier number to work with if it was rounded to only one digit in the ten millions place, so round 51,000,000 to 50,000,000.

Step 2 Determine from the chart the number of visitors who were from Japan.

According to the chart, 5,000,000 visitors to the United States were from Japan.

Step 3 To determine the percentage, divide.

number of visitors from Japan

___ total number of visitors

= 5,000,000

_ 50,000,000

= 0.1 or 10%

About 10% of the visitors to the United States in 2000 were from Japan.

Practice

1. Use the table at the right to find the total area Great Lakes

Great Lake Area ( mi 2 )

Lake Superior 31,698

Lake Huron 23,011

Lake Michigan 22,316

Lake Erie 9922

Lake Ontario 7320

of the Great Lakes.

2. The length of Fun Center’s go-kart track is 843 feet. If Nadia circled the track 9 times, about how many feet did she travel?

3. The Student Council is making pizzas to sell at the football game on Friday. Each pizza requires

2 1 _ 4 cups of cheese. If Student Council members

make 25 pizzas, how many cups ofcheese will they need?

4. In Florida, National Parks, State Parks, and Type of Park Area (in acres)

National Parks 2,571,164.45

State Parks 890,000

State Forests 723,000

Source: RAND Florida

State Forests have acreage shown in the table. If the total land and water area is 65,754.59 square miles, about what percentage of the total area is parks and forests? Use 1 square mile = 640 acres.

Visitors flock to USACanada14.6Mexico10.3Japan5.0U.K.4.7

Source: Travel Industry Association

Solve each problem by using estimation.



Problem-Solving Strategy: Eliminate Unnecessary InformationA useful problem-solving strategy is to learn how to eliminate unnecessary information. If there is a diagram, it is important to determine if all or some of the information is necessary to find a solution.

EXAMPLE

Twila is making a quilt that shows a house repeating on each block of the quilt. Which information is unnecessary to find the area of the white door of the house?

The dimensions needed to find the area of the door are the length and width of

the door. So, the dimensions of 2 1 _ 2 inches

by 5 1 _ 2 inches are needed. The other

dimensions, such as the width of the window or the size of the square, are unnecessary.

Practice

Solve each problem by eliminating unnecessary information.

1. Which information is not Recordlows

Source: National Oceanic and Atmospheric Administration

Lowestin USA

Lowest incontiguous48 states

Lowesteast of

Miss. River

–80°Prospect Creek,

AlaskaJan. 23, 1971

–55°Allagash,

MaineJan. 14, 1999

–70°Rogers Pass,

Mont.Jan. 20, 1954

necessary to find the temperature difference between the record lows in Alaska and Maine?

2. The Gemini North telescope was placed in Mauna Kea, Hawaii, in the year 2000. The Gemini South telescope was placed in Cerro Pachon, Chili, in the year 2001. Each of the twin telescopes are 8.1 meters in diameter. What information is not necessary to find the circumference of the base of the telescopes?

3. Which information is not necessary to find the difference in height between the tallest building and the 4th tallest building?

Rank Building, city Year StoriesHeight

m ft

1. Taipei 101, Taipei, Taiwan 2004 101 508 1,667

2. Petronas Tower 1, Kuala Lumpur, Malaysia 1998 88 452 1,483

3. Petronas Tower 2, Kuala Lumpur, Malaysia 1998 88 452 1,483

4. Sears Tower, Chicago 1974 110 442 1,451

5. Jin Mao Building, Shanghai 1999 88 421 1,381

Source: Council on Tall Building and Urban Habitat

Prob

lem

-Sol

ving

Han

dboo

k


Problem-Solving Strategy: Write an EquationA natural outcome of recognizing mathematical patterns and organizing data is to write an equation. Look at a set of data or read a word problem to determine which values are constants and which values vary. Figure out the dependent and independent variables in order to write an equation to reflect the given situation.

EXAMPLE

For every $10 gift card sold, the theater department at Wallace High School earns $1.25. Write an equation to represent the amount raised based on the number of cards sold.

Step 1 Make a table of data to represent the number of cards sold and the amount of money raised.

Step 2 Find the value that varies.The value that varies is the number of cards sold and the amount raised based on the number of cards sold.

Step 3 Find the value that is constant for each card sold. The value that is constant for each card sold is the amount of money raised per card, $1.25. This is the slope of the line.

Step 4 Write the equation that shows how the total amount changes based on the number of cards sold.

The equation is y = 1.25x.

Practice

Solve each problem by writing an equation.

1. Write an equation that can be used

Type of VeteransTotal Number of Veterans 23,425,051

Gulf War veterans 18.7%

Vietnam-era veterans 33.5%

Korean War veterans 13.3%

World War II veterans 13.9%

Source: U.S. Census Bureau

to find the number of Korean War Veterans.

2. The top five states in land area are given in the table. Write an equation to find how much larger Alaska’s land area is compared to Montana.

3. Increasingly, Internet users are using broadband Broadband at Home

Survey date Users (in millions)

June 2000 6

May 2005 66

Source: Pew Internet Project

Internet in their homes. Write an equation for the slope of this data in the five years shown.

4. Iceland spent approximately 8.8% of its gross domestic product (GDP) on public health expenditures in 2006, the highest percentage of all countries. If Iceland had a GDP of $11,380,000,000 in 2006, write an equation to show how much money was spent on public health expenditures.

Number of Cards Amount of Money ($)

1 1.25

2 2.50

3 3.75

4 5.00

Extra Practice

Extra Practice 815

Extra Practice

Variables and Expressions (pp. 5–9)Lesson 1-1

Write an algebraic expression for each verbal expression.

1. the sum of b and 21 2. the product of x and 7

3. the sum of 4 and 6 times a number z 4. the sum of 8 and -2 times n

5. one-half the cube of a number x 6. four-fifths the square of m

Write a verbal expression for each algebraic expression.

7. 2n 8. 10 7 9. m 5

10. xy 11. 5 n 2 - 6 12. 9 a 3 + 1

13. 17 - 4 m 5 14. 12 z 2

_ 5 15. 3 x 2 - 2x

Order of Operations (pp. 10–15)Lesson 1-2

Evaluate each expression.

1. 3 + 8 ÷ 2 - 5 2. 4 + 7 · 2 + 8 3. 5(9 + 3) - 3 · 4

4. 9 - 3 2 5. (8 - 1) · 3 6. 4 (5 - 3) 2

7. 3(12 + 3) - 5 · 9 8. 5 3 + 6 3 - 5 2 9. 16 ÷ 2 · 5 · 3 ÷ 6

10. 7 ( 5 3 + 3 2 ) 11. 9 · 4 + 2 · 6

_ 6 · 4

12. 25 - 1 _ 3 (18 + 9)

13. 2 4 14. 10 2 15. 7 3

16. 20 3 17. 3 6 18. 4 5

19. 10 6 20. 3 5 21. 15 3

Evaluate each expression if a = 2, b = 5, x = 4, and n = 10.

22. 8a + b 23. 48 + ab 24. a(6 - 3n)

25. bx + an 26. x 2 - 4n 27. 3b + 16a - 9n

28. n 2 + 3(a + 4) 29. (2x) 2 + an - 5b 30. [a + 8(b - 2)] 2 ÷ 4

31. ( 3b 2 ) 3 + 2x 32. b 2 + 3 n 3 - 4(x - 8 ) 2 33. [x + 2n(3a + 4)] - a 4

Properties of Numbers (pp. 16–22)Lesson 1-3

Evaluate each expression using the properties of numbers. Name the property used in each step.

1. 2 _

3 [15 ÷ (12 - 2)] 2. 7 _

4 ⎡

⎢

⎣

4 · (

1 _ 8 · 8

)

⎤

�

⎦

3. [(18 ÷ 3) · 0] · 10

4. 23 + 8 + 37 + 12 5. 19 + 46 + 81 + 54 6. 10.25 + 2.5 + 3.75

7. 22.5 + 17.6 + 44.5 8. 2 1 _ 3

+ 6 + 3 2 _ 3 + 4 9. 5 6 _

7 + 15 + 4 1 _

7 + 25

10. 6 · 8 · 5 · 3 11. 18 · 5 · 2 · 5 12. 0.25 · 7 · 8

13. 90 · 12 · 0.5 14. 5 1 _ 3 · 4 · 6 15. 4 5 _

6 · 10 · 12

Extr

a Pr

actic

e

816 Extra Practice

The Distributive Property (pp. 23–29)Lesson 1-4

Use the Distributive Property to rewrite each expression. Then evaluate.

1. 5(2 + 9) 2. 8(10 + 20) 3. 6(y + 4)

4. 9(3n + 5) 5. 32 (

x - 1 _ 8 )

6. c(7 - d)

Simplify each expression. If not possible, write simplified.

7. 13a + 5a 8. 21x - 10x 9. 8(3x + 7)

10. 4m - 4n 11. 3(5am - 4) 12. 15 x 2 + 7 x 2

13. 9 y 2 + 13 y 2 + 3 14. 11 a 2 - 11 a 2 + 12 a 2 15. 6a + 7a + 12b + 8b

16. 5a + 6b + 7a 17. 8x + 4y + 9x 18. 3a + 5b + 2c + 8b

Equations (pp. 31–37)Lesson 1-5

Find the solution of each equation if the replacement sets are x = {0, 2, 4, 6, 8} and y = {1, 3, 5, 7, 9}.

1. x - 4 = 4 2. 25 - y = 18 3. 3x + 1 = 25

4. 5y - 4 = 11 5. 14 = 96 _ x + 2 6. 0 =

y _

3 - 3

Solve each equation.

7. x = 27 + 9

_ 2 8. 18 - 7

_ 13 - 2

= y 9. n = 6(5) + 3

_ 2(4) + 3

10. 5(4) - 6

_ 2 2 + 3

= z 11. 7 2 + 9(2 + 1)

__ 2(10) - 1

= t 12. a = 3 3 + 5 2

_ 2(3 - 1)

Relations (pp. 38–44)Lesson 1-6

Describe what is happening in each graph.

1. The graph shows the average 2. The graph shows the speed of monthly high temperatures for a a roller coaster car during a city over a one-year period. two-minute ride.

Tem

pera

ture

Month

Spee

d

Time

Express the relation shown in each table, mapping, or graph as a set of ordered

pairs. Then describe the domain and range.

3. x y

1 3

2 4

3 5

4 6

5 7

4. x y

-4 1

-2 3

0 1

2 3

4 1

5. X Y

-1-2-6

541

Extra Practice

Extra Practice 817

Functions (pp. 45–52)Lesson 1-7

Determine whether each relation is a function. Explain.

1. x y

1 3

2 5

1 -7

2 9

2. X Y

-23

-4-2

02

3. y

x

4. x 2 + y = 11 5. y = 2 6. {(-2, 4), (1, 3), (5, 2), (1, 4)}

If f(x) = 2x + 5 and g(x) = 3 x 2 - 1, find each value.

7. f(-4) 8. g(2) 9. f(3) - 5 10. g(a + 1)

Logical Reasoning and Counterexamples (pp. 54–59)Lesson 1-8

Identify the hypothesis and conclusion of each statement.

1. If an animal is a dog, then it barks.

2. If a figure is a pentagon, then it has five sides.

3. If 3x - 1 = 8, then x = 3.

4. If 0.5 is the reciprocal of 2, then 0.5 · 2 = 1.

Identify the hypotheses and conclusion of each statement. Then write the statement in if-then form.

5. A square has four congruent sides. 6. 6a + 10 = 34 when a = 4.

7. The video store is open every night. 8. The band will not practice on Thursday.

Find a counterexample for each conditional statement.

9. If the season is spring, then it does 10. If you live in Portland, then you live innot snow. Oregon.

11. If 2y + 4 = 10, then y < 3. 12. If a 2 > 0, then a > 0.

Writing Equations (pp. 75–80)Lesson 2-1

Translate each sentence into a formula.

1. A number z times 2 minus 6 is the same as m divided by 3.

2. The cube of a decreased by the square of b is equal to c.

3. Twenty-nine decreased by the product of x and y is the same as z.

4. The perimeter P of an isosceles triangle is the sum of twice the length of leg a and the length of the base b.

5. Thirty increased by the quotient of s and t is equal to v.

6. The area A of a rhombus is half the product of lengths of the diagonals a and b.

Translate each equation into a sentence.

7. 0.5x + 3 = -10 8. n _ -6

= 2n + 1 9. 18 - 5h = 13h

10. n 2 = 16 11. 2 x 2 + 3 = 21 12. m _ n + 4 = 12

Extr

a Pr

actic

e

818 Extra Practice

Solving One-Step Equations (pp. 81–89)Lesson 2-2

Solve each equation. Check your solution.

1. -2 + g = 7 2. 9 + s = -5 3. -4 + y = -9

4. m + 6 = 2 5. t + (-4) = 10 6. v - 7 = -4

7. a - (-6) = -5 8. -2 - x = -8 9. d + (-44) = -61

10. b - (-26) = 41 11. p - 47 = 22 12. -63 - f = -82

13. 7p = 35 14. -3x = -24 15. 2y = -3

16. 62y = -2356 17. a _ -6

= -2 18. c _ -59

= -7

19. 7 _

10 - a = 1 _

2 20. f -

(

- 1 _ 8 )

= 3 _ 10

21. -4 5 _ 12

= t - (

-10 1 _ 36

)

22. x + 3 _ 8 = 1 _

4 23. 1 7 _

16 + s = 9 _

8 24. 17 8 _

9 = d +

(

-2 5 _ 6 )

25. - 5 _

9 r = 7

1 _

2 26. 2 1 _

6 j = 5 1 _

5 27. 3 = 1 7 _

11 q

Solving Multi-Step Equations (pp. 90–96)Lesson 2-3


1. 2x - 5 = 3 2. 4t + 5 = 37 3. 7a + 6 = -36

4. 47 = -8g + 7 5. -3c - 9 = -24 6. 5k - 7 = -52

7. 5s + 4s = -72 8. 3x - 7 = 2 9. 8 + 3x = 5

10. -3y + 7.569 = 24.069 11. 7 - 9.1f = 137.585 12. 6.5 = 2.4m - 4.9

13. n _

5 + 6 = -2 14. d

_ 4 - 8 = -5 15. - 4 _

13 y - 7 = 6

16. p + 3

_ 10

= 4 17. h - 7 _

6 = 1 18.

5f + 1 _

8 = -3

19. 4n - 8 _

-2 = 12 20. -3t - 4

_ 2 = 8 21. 4.8a - 3 + 1.2a = 9

Solving Equations with the Variable on Each Side (pp. 97–102)Lesson 2-4


1. 5x + 1 = 3x - 3 2. 6 - 8n = 5n + 19

3. -3z + 5 = 2z + 5 4. 2 _

3 h + 5 = -4 - 1 _

3 h

5. 1 _

2 a - 4 = 3 - 1 _

4 a 6. 6(y - 5) = 18 - 2y

7. -28 + p = 7(p - 10) 8. 1 _

3 (b - 9) = b + 9

9. -4x + 6 = 0.5(x + 30) 10. 4(2y - 1) = -8(0.5 - y)

11. 1.9s + 6 = 3.1 - s 12. 2.85y - 7 = 12.85y - 2

13. 2.9m + 1.7 = 3.5 + 2.3m 14. 3(x + 1) - 5 = 3x - 2

15. x _

2 - 1 _

3 = x _

3 - 1 _

2 16. 6v - 9

_ 3 = v

17. 3t + 1 _

4 = 3 _

4 t - 5 18. 0.4(x - 12) = 1.2(x - 4)

19. 3y - 4 _ 5 = 1 _

3 y 20. 3

_ 4 x - 4 = 7 + 1 _

2 x

21. -0.2(1 - x) = 2(4 + 0.1x) 22. 3.2(y + 1) = 2(1.4y - 3)

Extra Practice

Extra Practice 819

Solving Equations Involving Absolute Value (pp. 103–109)Lesson 2-5

Solve each open sentence. Then graph the solution set.

1. ⎪c - 5⎥ = 4 2. ⎪e + 3⎥ = 7 3. ⎪

4 - g⎥

= 6

4. ⎪10 - k⎥ = 8 5. ⎪

2j + 4⎥

= 12 6. ⎪2r - 6⎥ = 10

7. ⎪6 - 3w⎥ = 8 8. ⎪7 + 2x⎥ = 14 9. ⎪4z + 6⎥ = 12

Evaluate each expression when a = 7, b = 5, and c = -2.

10. ⎪a - b⎥ 11. ⎪b - a⎥ 12. ⎪2a + c⎥

13. -

⎪c⎥ + ⎪b⎥ 14. -

⎪b⎥ + ⎪a + c⎥ 15. ⎪4b - c⎥

Ratios and Proportions (pp. 111–118)Lesson 2-6

Solve each proportion. If necessary, round to the nearest hundredth.

1. 4 _

5 = x _

20 2.

b _

63 = 3 _

7 3.

y _

5 = 3 _

4

4. 7 _

4 = 3 _

a 5. t - 5

_ 4 = 3 _

2 6. x

_ 9 = 0.24

_ 3

7. n _ 3 =

n + 4 _

7 8.

12q _

-7 = 30

_ 14

9. 1 _

y - 3 = 3

_ y - 5

10. x _

8.71 = 4

_ 17.42

11. a - 3 _

8 = 3 _

4 12.

6p - 2 _

7 =

5p + 7 _

8

13. 2 _

9 =

k + 3 _

2 14.

5m - 3 _

4 =

5m + 3 _

6 15.

w - 5 _

4 =

w + 3 _

3

16. 96.8

_ t = 12.1 _

7 17.

r - 1 _

r + 1 = 3 _

5 18. 4n + 5

_ 5 =

2n + 7 _

7

Determine whether each pair of ratios are equivalent ratios. Write yes or no.

19. 3 _

4 , 7 _

8 20. 3.8

_ 2 , 4.1

_ 4 21. 8

_ 9 , 17.6

_ 19.8

22. 5 _

6 , 20

_ 24

23. 5 _

4 , 30.5

_ 24.4

24. 1 _

3 , 3 _

1

Percent of Change (pp. 119–125)Lesson 2-7

State whether each percent of change is a percent of increase or a percent of decrease. Then find each percent of change. Round to the nearest whole percent.

1. original: $100 2. original: 62 acres 3. original: 322 people new: $67 new: 98 acres new: 289 people

4. original: 78 pennies 5. original: $212 6. original: 35 mph new: 36 pennies new: $230 new: 65 mph

Find the final price of each item.

7. television: $299 8. book: $15.95 9. software: $36.90 discount: 20% sales tax: 7% sales tax: 6.25%

10. boots: $49.99 11. jacket: $65 12. backpack: $28.95 discount: 15% discount: 30% discount: 10%

sales tax: 3.5% sales tax: 4% sales tax: 5%

Extr

a Pr

actic

e

820 Extra Practice

Literal Equations and Dimensional Analysis (pp. 126–131)Lesson 2-8

Solve each equation or formula for x.

1. x + r = q 2. ax + 4 = 7 3. 2bx - b = -5

4. x - c _ c + a = a 5. x + y

_ c = d 6. ax + 1 _

2 = b

7. d(x - 3) = 5 8. nx - a = bx + d 9. 3x - r = r (-3 + x)

10. y = 5 _ 9 (x - 32) 11. A = 1 _

2 h(x + y) 12. A = 2π r 2 + 2πrx

Solve each equation or formula for the variable indicated.

13. S = 2b(a + c) + 2ac, for b 14. g(h + 8) = -j, for h 15. 11n + p

__ t = 8, for p

16. u - 10v __ 7 = w, for u 17.

9x - y __

z - 10 = 12, for x 18. 2k - 3

_ m + p = 5, for k

19. 14h + j = 2h, for h 20. -18k + m = 22k, for k 21. 39k + 3j = -6m, for j

Weighted Averages (pp. 132–138)Lesson 2-9

1. ADVERTISING An advertisement for grape drink claims that the drink contains 10% grape juice. How much pure grape juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% grape juice?

2. GRADES In Ms. Pham’s social studies class, a test is worth four times as much as homework. If a student has an average of 85% on tests and 95% on homework, what is the student’s average?

3. ENTERTAINMENT At the Golden Oldies Theater, tickets for adults cost $5.50 and tickets for children cost $3.50. How many of each kind of ticket were purchased if 21 tickets were bought for $83.50?

4. FOOD Wes is mixing peanuts and chocolate pieces. Peanuts sell for $4.50 a pound and the chocolate sells for $6.50 a pound. How many pounds of chocolate mixes with 5 pounds of peanuts to obtain a mixture that sells for $5.25 a pound?

5. TRAVEL Missoula and Bozeman are 210 miles apart. Sheila leaves Missoula for Bozeman and averages 55 miles per hour. At the same time, Casey leaves Bozeman and averages 65 miles per hour as he drives to Missoula. When will they meet? How far will they be from Bozeman?

Graphing Linear Equations (pp. 153–160)Lesson 3-1

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form.

1. 3x = 2y 2. 2x - 3 = y 2 3. 4x = 2y + 8

4. 5x - 7y = 2x - 7 5. 2x + 5x = 7y + 2 6. 1 _ x + 5 _ y = -4

Graph each equation by using the x- and y-intercepts or by making a table.

7. 3x + y = 4 8. y = 3x + 1 9. 3x - 2y = 12 10. 2x - y = 6

11. 2x - 3y = 8 12. y = -2 13. y = 5x - 7 14. x = 4

15. x + 1 _ 3 y = 2 16. 5x - 2y = 8 17. 4.5x + 2.5y = 9 18. 1 _

2 x + 3y = 12

Extra Practice

Extra Practice 821

Solving Linear Equations by Graphing (pp. 161–168)Lesson 3-2


1. -x + 6 = 0 2. 8x + 2 = 0 3. 4x + 3 = -2 + 4x

4. -2x + 5 = 5 5. 3 = 4x - 1 6. 1 _

2 x + 5 = -1

7. 6x - 4 = 8 + 6x 8. 1 _

2 = 3x - 4 9. 7 = -x - 4

Rate of Change and Slope (pp. 170–178)Lesson 3-3

Find the slope of the line that passes through each pair of points.

1. y

x

(24, 24)

(22, 0)

2. y

x

(24, 2)

(0, 21)

3. (-2, 2), (3, -3) 4. (-2, -8), (1, 4) 5. (3, 4), (4, 6) 6. (-5, 4), (-1, 11)

7. (18, -4), (6, -10) 8. (-4, -6), (-4, -8) 9. (0, 0), (-1, 3) 10. (-8, 1), (2, 1)

Find the value of r so the line that passes through each pair of points has the given slope.

11. (-1, r), (1, -4), m = -5 12. (r, -2), (-7, -1), m = - 1 _ 4

Direct Variation (pp. 180–186)Lesson 3-4

Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points.

1. y

x(0, 0)

(3, 2)

y = x23

2. y

x

(0, 0)

(22, 3)

y = - x32

3. y

(0, 0)(25, 1)

y = - x15

Graph each equation.

4. y = 5x 5. y = -6x 6. y = - 4 _ 3 x

Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.

7. If y = 45 when x = 9, find y when x = 7.

8. If y = -7 when x = -1, find x when y = -84.

Extr

a Pr

actic

e

822 Extra Practice

Arithmetic Sequences as Linear Functions (pp. 187–194)Lesson 3-5

Determine whether each sequence is an arithmetic sequence. Write yes or no. Explain.

1. -2, -1, 0, 1, … 2. 3, 5, 8, 12, … 3. 2, 4, 8, 16, …

4. -21, -16, -11, -6, … 5. 0, 0.25, 0.5, 0.75, … 6. 1 _

3 , 1 _

9 , 1 _

27 , 1 _

81 , …

Find the next three terms of each arithmetic sequence.

7. 3, 13, 23, 33, … 8. -4, -6, -8, -10, … 9. -2, -1.4, -0.8, -0.2, …

10. 5, 13, 21, 29, … 11. 3 _

4 , 7 _

8 , 1, 9 _

8 , … 12. - 1 _

3 , - 5 _

6 , - 4 _

3 , - 11

_ 6 , …

Write an equation for the nth term of the arithmetic sequence. Then graph the first five terms in the sequence.

13. -3, 1, 5, 9, … 14. 25, 40, 55, 70, … 15. -9, -3, 3, 9, … 16. -3.5, -2, -0.5, …

Proportional and Nonproportional Relationships (pp. 195–200)Lesson 3-6

Write an equation in function notation for each relation.

1. y

x

2. y

x

3. y

x

4. y

x

The table shows the number of cups of flour Cups of flour 4 8 12 16

Batches of brownies 1 2 3 4used to make batches of brownies.

5a. Write an equation for the data given.

5b. Graph the equation.

5c. Find the number of cups of flour needed for 6 batches of brownies.

Graphing Equations in Slope-Intercept Form (pp. 214–221)Lesson 4-1

Write an equation, in slope-intercept form, of the line with the given slope and y-intercept.

1. m: 5, y-intercept: -15 2. m: -6, y-intercept: 3 3. m: 0.3, y-intercept: -2.6

4. m: - 4 _ 3 , y-intercept: 5 _

3 5. m: - 2 _

5 , y-intercept: 2 6. m: 7 _

4 , y-intercept: -2

Write an equation in slope-intercept form for each graph shown.

7. y

x

(2, 1)

(0, 3)

8. y

x

(22, 22) (0, 23)

9. y

x

(0, 2)(23, 1)

Graph each equation.

10. y = 5x - 1 11. y = -2x + 3 12. 3x - y = 6

Extra Practice

Extra Practice 823

Writing Equations in Slope-Intercept Form (pp. 224–230)Lesson 4-2

Write an equation of the line that passes through the given point and has the given slope.

1. (0, 0); m = -2 2. (-3, 2); m = 4

3. (0, 5); m = -1 4. (-2, 3); m = -

1 _

4

5. (1, -5); m = 2 _ 3 6.

(

1 _

2 , 1 _

4 )

; m = 8

Write an equation of the line that passes through each pair of points.

7. (-1, 7), (8, -2) 8. (4, 0), (0, 5)

9. (8, -1), (7, -1) 10. (-2, 3), (1, 3)

11. (0, 0), (-4, 3) 12. (

- 1 _ 2 , 1 _

2 )

, (

1 _ 4 , 3 _

4 )

Writing Equations in Point-Slope Form (pp. 231–236)Lesson 4-3

Write an equation in point-slope form for the line that passes through each point with the given slope. Then graph the equation.

1. (5, -2), m = 3 2. (0, 6), m = -2

3. (-3, 1), m = 0 4. (-2, -4), m = 3 _ 4

Write each equation in standard form.

5. y + 3 = 2(x - 4) 6. y + 3 = -

1 _

2 (x + 6)

7. y - 4 = -

2 _

3 (x - 5) 8. y + 2 = 4 _

3 (x - 6)

9. y - 1 = 1.5(x + 3) 10. y + 6 = -3.8(x - 2)

Write each equation in slope-intercept form.

11. y - 1 = -2(x + 5) 12. y + 3 = 4(x - 1)

13. y - 6 = -4(x - 2) 14. y + 1 = 4 _ 5 (x + 5)

15. y - 2 = -

3 _

4 (x - 2) 16. y + 1 _

4 = 2 _

3 (

x + 1 _ 2 )

Parallel and Perpendicular Lines (pp. 237–243)Lesson 4-4

Write the slope-intercept form of an equation for the line that passes through the given point and is parallel to the graph of each equation. Then write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of each equation.

1. (1, 6), y = 4x - 2 2. (4, 6), y = 2x - 7

3. (-3, 0), y = 2 _ 3 x + 1 4. (5, -2), y = -3x - 7

5. (0, 4), 3x + 8y = 4 6. (2, 3), x - 5y = 7

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

7. y = -2x + 11 8. 3y = 2x + 14 9. y = -5xy + 2x = 23 2x - 3y = 2 y = 5x - 18

Extr

a Pr

actic

e

824 Extra Practice

Scatter Plots and Lines of Fit (pp. 245–252)Lesson 4-5

Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a correlation, describe its meaning in the situation.

1.

0

Value and Age of CarValue and Age of Car

25

20

15

10

5Valu

e (th

ousa

nds)

Age of Car (years)1 2 3 4 5

2.

Source: ESPN Almanac

Winning Super Bowl ScoresWinning Super Bowl Scores

Win

ning

Sco

re 50

40

30

20

10

Year19

92019

9419

9619

9820

0020

0220

0420

06

Regression and Median-Fit Lines (pp. 253–260)Lesson 4-6

1. COMPUTERS The media center is keeping track of student computer use to determine if they need to purchase more computers. There are 6 computers in the center. The results of the 10-day tracking period are recorded in the table. Write an equation for the regression line for the data. Then find the correlation coefficient.

Student Computer UseDay 1 2 3 4 5 6 7 8 9 10

Number of Students 48 62 75 70 32 52 70 63 81 40

2. STOCKS For a class project, the students were asked to keep track of a stock price for a company of local interest. They were to record the closing price of the stock at the end of each Friday for 8 weeks. Marcus was out of town one week and missed the price for week 4. Find the equation for the data, and approximate the

price for week 4.

Weekly Closing Stock Price for Barney’s InternationalWeek 1 2 3 5 6 7 8

Closing Price 29 27 29 33 34 33 34

Special Functions (pp. 261–269)Lesson 4-7

Graph each function.

1. f(x) = -3[x] 2. g(x) = [4x] 3. h(x) = 2[x] - 3

4. f(x) = ⎪x + 2⎥ 5. g(x) = ⎪3x - 1⎥ 6. f(x) = { -2x if x < 3 { x + 1 if x ≥ 3

7. PARKING Short-term parking at the airport Short-Term Parking Fees

Hours Fees

0 < h ≤ 1 _ 2 $2

1 _ 2 < h ≤ 1 $3

1 < h ≤ 1 1 _ 2 $4

is $2 for the first half-hour and $1 for each half-hour after that. Complete the table and then draw a graph that represents this information.

Extra Practice

Extra Practice 825

Solving Inequalities by Addition and Subtraction (pp. 283–288)Lesson 5-1

Solve each inequality. Check your solution, and then graph it on a number line.

1. c + 9 ≤ 3 2. d - (-3) < 13 3. z - 4 > 20 4. h - (-7) > -2

5. -11 > d - 4 6. 2x > x - 3 7. 2x - 3 ≥ x 8. 16 + w < -20

9. 14p > 5 + 13p 10. -7 < 16 - z 11. 1.1v - 1> 2.1v - 3 12. 1 _ 2 t + 1 _

4 ≥ 3 _

2 t - 2 _

3

13. 9x < 8x - 2 14. -2 + 9n ≤ 10n 15. a - 2.3 ≥ -7.8 16. 5z - 6 > 4z

Define a variable, write an inequality, and solve each problem. Check your solution.

17. The sum of a number and negative six is greater than 9.

18. Negative five times a number is less than the sum of negative six times the number and 12.

Solving Inequalities by Multiplication and Division (pp. 290–295)Lesson 5-2

Solve each inequality. Check your solution.

1. 7b ≥ -49 2. -5j < -60 3. w

_ 3 > -12 4.

p _

5 < 8

5. -8f < 48 6. -0.25t ≥ -10 7. g _

-8 < 4 8. -4.3x < -2.58

9. 4c ≥ -6 10. 6 ≤ 0.8n 11. 2 _

3 m ≥ -22 12. -25 > -0.05a

13. -15a < -28 14. - 7 _ 9 x < 42 15. 0.375y ≤ 32 16. -7y ≥ 91

Define a variable, write an inequality, and solve each problem. Then check your solution.

17. Negative one times a number is greater than -7.

18. Three fifths of a number is at least negative 10.

19. Seventy-five percent of a number is at most 100.

Solving Multi-Step Inequalities (pp. 296–301)Lesson 5-3

Solve each inequality. Check your solution.

1. 3y - 4 > -37 2. 7s - 12 < 13

3. -5q + 9 > 24 4. -6v - 3 ≥ -33

5. -2k + 12 < 30 6. -2x + 1< 16 - x

7. 15t - 4 > 11t - 16 8. 13 - y ≤ 29 + 2y

9. 5q + 7 ≤ 3(q + 1) 10. 2(w + 4) ≥ 7(w - 1)

11. -4t - 5 > 2t + 13 12. {

2t + 5

_ 3

}

< -9

13. z _

4 + 7 ≥ -5 14. 13r - 11 > 7r + 37

15. 8c - (c - 5) > c + 17 16. -5(k + 4) ≥ 3(k - 4)

17. 9m + 7 < 2(4m - 1) 18. 3(3y + 1) < 13y - 8

19. 5x ≤ 10(3x + 4) 20. 3 (

a + 2 _ 3 )

≥ a - 1

Extr

a Pr

actic

e

826 Extra Practice

Solving Compound Inequalities (pp. 304–309)Lesson 5-4

Solve each compound inequality. Then graph the solution set.

1. 2 + x < -5 or 2 + x > 5 2. -4 + t > -5 or -4 + t < 7

3. 3 ≤ 2g + 7 and 2g + 7 ≤ 15 4. 2v - 2 ≤ 3v and 4v - 1 ≥ 3v

5. 3b - 4 ≤ 7b + 12 and 8b - 7 ≤ 25 6. -9 < 2z + 7 < 10

7. 5m - 8 ≥ 10 - m or 5m + 11 < -9 8. 12c - 4 ≤ 5c + 10 or -4c - 1 ≤ c + 24

9. 2h - 2 ≤ 3h ≤ 4h - 1 10. 3p + 6 < 8 - p and 5p + 8 ≥ p + 6

11. 2r + 8 > 16 - 2r and 7r + 21< r - 9 12. -4j + 3 < j + 22 and j - 3 < 2j - 15

13. 2(q - 4) ≤ 3(q + 2) or q - 8 ≤ 4 - q 14. 1 _

2 w + 5 ≥ w + 2 ≥ 1 _

2 w + 9

15. n - (6 - n) > 10 or -3n - 1 > 20 16. -(2x + 5) ≤ x + 5 ≤ 2x - 9

17. WIND SPEED The Fujita Scale (F-scale) is the official F-Scale Wind Speed

F0 40–72 mph

F1 73–112 mph

F2 113–157 mph

F3 158–206 mph

F4 207–260 mph

F5 261–318 mph

classification system for tornado damage. One factor used to classify a tornado is wind speed. Use the information in the table to write an inequality for the range of wind speeds of an F3 tornado.

Inequalities Involving Absolute Value (pp. 310–314)Lesson 5-5

Solve each inequality. Then graph the solution set.

1. ⎪x + 4⎥ < 10 2. ⎪

y - 3⎥

≥ 3 3. ⎪2x + 5⎥ < -2

4. ⎪

2x - 3

_ 5

⎥

≥ 4 5. ⎪

3m - 2

_ 2

⎥

≤ -7 6. ⎪

2n + 8

_ 3

⎥

> -2

7. ⎪5v + 2⎥ > -4 8. ⎪w - 8⎥ ≤ -14 9. ⎪3x + 2⎥ < -8

10. ⎪

4m + 5

_ 3

⎥

≥ 5 11. ⎪ y + 4

_ 5

⎥ < -4 12.

⎪

3h - 5

_ 2

⎥

> -5

Graphing Inequalities in Two Variables (pp. 315–320)Lesson 5-6

Determine which ordered pairs are part of the solution set for each inequality.

1. x + y ≥ 0, {(0, 0), (1, -3), (2, 2), (3, -3)}

2. 2x + y ≤ 8, {(0, 0), (-1, -1), (3, -2), (8, 0)}

Graph each inequality.

3. y ≤ -2 4. x < 4 5. x + y < -2

6. x + y ≥ -4 7. y > 4x - 1 8. 3x + y > 1

9. DELIVERIES A delivery truck with a 4000-pound weight limit is transporting televisions that weigh 77 pounds each and microwaves that weigh 55 pounds each.

a. Defi ne variables and write an inequality for this situation.

b. Will the truck be able to deliver 35 televisions and 25 microwaves at once?

Explain.

Extra Practice

Extra Practice 827

Graphing Systems of Equations (pp. 333–339)Lesson 6-1

Graph each system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

1. y = 3x 2. x = -2y 3. y = x + 4 4x + 2y = 30 x + y = 1 3x + 2y = 18

4. x + y = 6 5. x + y = 6 6. y = -3xx - y = 2 3x + 3y = 3 4x + y = 2

7. 2x + y = 8 8. 1 _

5 x - y = 12

_ 5 9. x + 2y = 0

x - y = 4 3x - 5y = 6 y + 3 = -x

10. x + 2y = -9 11. x + 1 _ 2 y = 3 12. 2 _

3 x + 1 _

2 y = 2

x - y = 6 y = 3x - 4 4x + 3y = 12

Substitution (pp. 342–347)Lesson 6-2

Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solutions or infinitely many solutions.

1. y = x 2. y = 7 - x 3. x = 5 - y 5x = 12y 2x - y = 8 3y = 3x + 1

4. 3x + y = 6 5. x - 3y = 3 6. 3x = -18 + 2y y + 2 = x 2x + 9y = 11 x + 3y = 4

7. x + 2y = 10 8. 2x = 3 - y 9. 6y - x = -36 -x + y = 2 2y = 12 - x y = -3x

10. 3 _

4 x + 1 _

3 y = 1 11. x + 6y = 1 12. 3x - 2y = 12

x - y = 10 3x - 10y = 31 3 _

2 x - y = 3

13. 2x + 3y = 5 14. x = 4 - 8y 15. 3x - 2y = -3 4x - 9y = 9 3x + 24y = 12 25x + 10y = 215

Elimination Using Addition and Subtraction (pp. 348–354)Lesson 6-3

Use elimination to solve each system of equations.

1. x + y = 7 2. 2x - y = 32 3. -y + x = 6 x - y = 9 2x + y = 60 y + x = 5

4. s + 2t = 6 5. x = y - 7 6. 3x + 5y = -16 3s - 2t = 2 2x - 5y = -2 3x - 2y = -2

7. x - y = 3 8. x + y = 8 9. 2s - 3t = -4 x + y = 3 2x - y = 6 s = 7 - 3t

10. -6x + 16y = -8 11. 3x + 0.2y = 7 12. 9x + 2y = 26 6x - 42 = 16y 3x = 0.4y + 4 1.5x - 2y = 13

13. x = y 14. 4x - 1 _ 3 y = 8 15. 2x - y = 3

x + y = 7 5x + 1 _ 3 y = 6

2 _

3 x - y = -1

Extr

a Pr

actic

e

828 Extra Practice

Elimination Using Multiplication (pp. 355–360)Lesson 6-4

Use elimination to solve each system of equations.

1. -3x + 2y = 10 2. 2x + 5y = 13 3. 5x + 3y = 4 -2x - y = -5 4x - 3y = -13 -4x + 5y = -18

4. 1 _

3 x - y = -1 5. 3x - 5y = 8 6. x - 0.5y = 1

1 _

5 x - 2 _

5 y = -1 4x - 7y = 10 0.4x + y = -2

7. x + 8y = 3 8. 4x - y = 4 9. 3y - 8x = 9 4x - 2y = 7 x + 2y = 3 y - x = 2

10. x + 4y = 30 11. 3x - 2y = 0 12. 9x - 3y = 5 2x - y = -6 4x + 4y = 5 x + y = 1

13. 2x - 7y = 9 14. 2x - 6y = -16 15. 6x - 3y = -9 -3x + 4y = 6 5x + 7y = -18 -8x + 2y = 4

Applying Systems of Linear Equations (pp. 362–368)Lesson 6-5

Determine the best method to solve each system of equations. Then solve the system.

1. y = 2x + 1 2. y = 5x - 8 3. x + 2y = -6 y = -3x + 1 y = 3x x = y + 3

4. 2x - 3y = 5 5. x = -1 6. 4x + y = 5 y = -6x y = 8 -4x - 2y = 9

7. -7x + 3y = -4 8. 4x - y = 11 9. 2y - x = -7 2x + 3y = 5 x + 2y = 5 x + 3y = 5

10. -13x + 8y = -6 11. -x + 7y = 9 12. 2x + 5y = 7 3x - 4y = 2 -4x + 6y = -8 5x - 2y = 13

13. 12x - 3y = 7 14. 6x = 5 15. 17x + 8y = -4 x = 2 + 13y 9y - 2x = 7 -8y - 2x = 9

Organizing Data Using Matrices (pp. 369–375)Lesson 6-6

Perform the indicated matrix operations. If the matrix does not exist, write impossible.

1. ⎡

⎢

⎣

3

-7

5

2 ⎤

�

⎦

+

⎡

⎢

⎣

-2

8

6

-1 ⎤

�

⎦

2. [0 -1 3] +

⎡

⎢

⎣

5

-2

-3

⎤

�

⎦

3. ⎡

⎢

⎣

45

63

36

29

18

5 ⎤

�

⎦

-

⎡

⎢

⎣

45

18

-2

9

36

10 ⎤

�

⎦

4. 4[-8 2 9] - 3[2 -7 6]

5. 5

⎡

⎢

⎣

6

5

-2

4 ⎤

�

⎦

- 2

⎡

⎢

⎣

6

5

-2

4 ⎤

�

⎦

+ 4

⎡

⎢

⎣

7

-4

-6

2 ⎤

�

⎦

6. 1.3

⎡

⎢

⎣

3.7

-5.4 ⎤

�

⎦

+ 4.1

⎡

⎢

⎣

6.4

-3.7 ⎤

�

⎦

- 6.2

⎡

⎢

⎣

-0.8

7.4

⎤

�

⎦

Use matrices A, B, C, D, and E to find the following.

A =

⎡

⎢

⎣

1

0

0

1 ⎤

�

⎦

, B =

⎡

⎢

⎣

-1

0

0

-1 ⎤

�

⎦

, C =

⎡

⎢

⎣

2

-3

-2

3 ⎤

�

⎦

, D =

⎡

⎢

⎣

-2

3

2

-3 ⎤

�

⎦

, E =

⎡

⎢

⎣

5

-2

-3

4 ⎤

�

⎦

7. A + B 8. C + D 9. A - B 10. 4B

11. D - C 12. E + 2A 13. D - 2B 14. 2A + 3E - D

Extra Practice

Extra Practice 829

Using Matrices to Solve Systems of Equations (pp. 376–381)Lesson 6-7

Write an augmented matrix equation for each system of equations.

1. 5a + 3b = 6 2. 3x + 4y = -8 3. m + 3n = 1 2a - b = 9 2x - 3y = 6 4m - n = -22

4. 4c - 3d = -1 5. x + 2y - z = 6 6. 2a - 3b - c = 4 5c - 2d = 39 -2x + 3y + z = 1 4a + b + c = 15

x + y + 3z = 8 a - b - c = -2

Solve each matrix equation or system of equations.

7. ⎡

⎢

⎣

3

2

4

-5

33

-1 ⎤

�

⎦

8. ⎡

⎢

⎣

-1

7

1

-6

0

3 ⎤

�

⎦

9. ⎡

⎢

⎣

1

0

0

1

-29

52 ⎤

�

⎦

10. 5x - y = 7 11. 3m + n = 4 12. 6c + 5d = 7 13. 3a - 5b = 1 8x + 2y = 4 2m + 2n = 3 3c - 10d = -4 a + 3b = 5

14. 2r - 7s = 24 15. x + y = -3 16. 2m - 3n = 3 17. x + y = 1 -r + 8s = -21 3x - 10y = 43 -4m + 9n = -8 2x - 2y = -12

Systems of Inequalities (pp. 382–387)Lesson 6-8

Solve each system of inequalities.

1. x ≤ 5 2. y < 3 3. x + y < 5 4. y + x < 2 y ≥ -3 y - x ≥ -1 x < 2 y ≥ x

5. x + y ≤ 2 6. y ≤ x + 4 7. y < 1 _ 3 x + 5 8. y + x ≥ 1

y - x ≤ 4 y - x ≥ 1 y > 2x + 1 y - x ≥ -1

9. ⎪x⎥ > 2 10. ⎪x - 3⎥ ≤ 3 11. 4x + 3y ≥ 12 12. y ≤ -1

⎪

y⎥

≤ 5 4y - 2x ≤ 6 2y - x ≥ -1 3x - 2y ≥ 6

Multiplying Monomials (pp. 401–407)Lesson 7-1

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.

1. n2 - 3 2. 53 3. 9a2b3 4. 15 - x2y

Simplify each expression.

5. a 5 (a) ( a 7 ) 6. ( r 3 t 4 ) ( r 4 t 4 ) 7. ( x 3 y 4 ) (x y 3 )

8. (b c 3 ) ( b 4 c 3 ) 9. (-3m n 2 ) (5 m 3 n 2 ) 10. ⎡

⎣

( 3 3 ) 2 ⎤

⎦

2

11. (3s3 t 2 ) (-4 s 3 t 2 ) 12. x 3 ( x 4 y 3 ) 13. (1.1 g 2 h 4 ) 3

14. -

3 _

4 a ( a 2 b 3 c 4 ) 15.

(

1 _

2 w 3

)

2 ( 6w 4 )

2 16. ⎡

⎣

(- 2 3 ) 3 ⎤

⎦

2

GEOMETRY Express the volume of each solid as a monomial.

17. 18. 19.

Extr

a Pr

actic

e

830 Extra Practice

Dividing Monomials (pp. 408–415)Lesson 7-2

Simplify. Assume that no denominator is equal to zero.

1. 610 _

67 2. b 6 c 5

_ b 3 c 2

3. (-a) 4 b 8

_ a 4 b 7

4. (-x) 3 y 3

_ x 3 y 6

5. 12a b 5 _

4 a 4 b 3 6. 24 x 5

_ -8 x 2

7. -9 h 2 k 4 _

18 h 5 j 3 k 4 8.

(

2 a 2 b 4

_ 3 a 3 b

)

2

9. a 5 b 0 a -7 10. ( -u -3 v 3 ) 2 _

( u 3 v) -3 11.

(

a 3

_ b 2

)

-3

12. (

2x _

y -3 )

-2

13. (-r) s 5

_ r -3 s -4

14. 28 a -4 b 0 _

14 a 3 b -1 15.

( j 2 k 3 m) 4 _

(j k 4

) -1

16. (

-2 x 4 y

_ 4 y 2

)

0

17. (

-18 x 0 a -3

_ -6 x -2 a -3

)

18. (

2 a 3 b -2

_ 2 -1 a -5 b 3

)

-1

19. (

5 n -1 m 2

_ 2n m -2

)

0

20. (3a b 2 c) -3

_ (2 a 2 b c 2 )

2

Scientific Notation (pp. 416–422)Lesson 7-3

Express each number in scientific notation.

1. 1,400,322 2. 134,490,000 3. 0.00009

4. 0.004500 5. 12,000,000 6. 0.0000233

Express each number in standard form.

7. 2.23 × 10 -2 8. 5.4 × 10 3 9. 3.334 × 10 -9

10. 4.7 × 10 -6 11. 5.22 × 10 4 12. 7.256 × 10 -1

Evaluate. Express the results in both scientific notation and standard form.

13. (2.3 × 10 -2 )(2.55 × 10 3 ) 14. (5.23 × 10 -7 )(8.2 × 10 5 )

15. 3.344 × 10 6

_ 4.2 × 10 -3

16. 2.644 × 10 -5

__ 3.2 × 10 -2

Polynomials (pp. 424–429)Lesson 7-4

State whether each expression is a polynomial. If so, identify it as a monomial, a binomial, or a trinomial.

1. 5 x 2 y + 3xy - 7 2. 0 3. 5 _ k - k 2 y 4. 3 a 2 x - 5a

Find the degree of each polynomial.

5. a + 5c 6. 14abcd - 6 d 3 7. a 3

_ 4 8. 10

9. -4 h 5 10. x 2

_ 3 - x _

2 + 1 _

5 11. -6 12. a 2 b 3 - a 3 b 2

Arrange the terms of each polynomial so that the powers of x are in ascending order.

13. 2 x 2 - 3x + 4 x 3 - x 5 14. x 3 - x 2 + x - 1 15. 2a + 3a x 2 - 4ax

16. -5b x 3 - 2bx + 4 x 2 - b 3 17. x 8 + 2 x 2 - x 6 + 1 18. cd x 2 - c 2 d 2 x + d 3

Arrange the terms of each polynomial so that the powers of x are in descending order.

19. 5 x 2 - 3 x 3 + 7 + 2x 20. -6x + x 5 + 4 x 3 - 20 21. 5b + b 3 x 2 + 2 _ 3 bx

22. 21 p 2 x + 3p x 3 + p 4 23. 3a x 2 - 6 a 2 x 3 + 7 a 3 - 8x 24. 1 _ 3 s 2 x 3 + 4 x 4 - 2 _

5 s 4 x 2

Extra Practice

Extra Practice 831

Adding and Subtracting Polynomials (pp. 433–438)Lesson 7-5

Find each sum or difference.

1. (3 a 2 + 5) + (4 a 2 - 1) 2. (5x - 3) + (-2x + 1)

3. (6z + 2) - (9z + 3) 4. (-4n + 7) - (-7n - 8)

5. (-7 t 2 + 4ts - 6 s 2) + (-5 t 2 - 12ts + 3 s 2 ) 6. (6 a 2 - 7ab - 4 b 2 ) - (2 a 2 + 5ab + 6 b 2 )

7. (4 a 2 - 10 b 2 + 7 c 2 ) + (-5 a 2 + 2 c 2 + 2b) 8. ( z 2 + 6z - 8) - (4 z 2 - 7z - 5)

9. (4d + 3e - 8f) - (-3d + 10e - 5f + 6) 10. (7g + 8h - 9) + (-g - 3h - 6k)

11. (9 x 2 - 11xy - 3 y 2 ) - ( x 2 - 16xy + 12 y 2 ) 12. (-3m + 9mn - 5n) + (14m - 5mn - 2n)

13. (6 - 7y + 3 y 2 ) + (3 - 5y - 2 y 2 ) + (-12 - 8y + y 2 )

14. (-7 c 2 - 2c - 5) + (9c - 6) + (16 c 2 + 3) + (-9 c 2 - 7c + 7)

Multiplying a Polynomial by a Monomial (pp. 439–444)Lesson 7-6

Find each product.

1. -3(8x + 5) 2. 3b(5b + 8) 3. 1.1a(2a + 7)

4. 1 _

2 x(8x - 6) 5. 7xy(5 x 2 - y 2 ) 6. 5y( y 2 - 3y + 6)

7. -ab(3 b 2 + 4ab - 6 a 2 ) 8. 4 m 2 (9 m 2 n + mn - 5 n 2 ) 9. 4s t 2 (-4 s 2 t 3 + 7 s 5 - 3s t 3 )


10. -3a(2a - 12) + 5a 11. 6(12 b 2 - 2b) + 7(-2 - 3b) 12. x(x - 6) + x(x - 2) + 2x

13. 11(n - 3) + 2( n 2 + 22n) 14. -2x(x + 3) + 3(x + 3) 15. 4m(n - 1) - 5n(n + 1)


16. -6(11 - 2x) = 7(-2 - 2x) 17. 11(n - 3) + 5 = 2n + 44

18. a(a - 6) + 2a = 3 + a(a - 2) 19. q(2q + 3) + 20 = 2q(q - 3)

20. w(w + 12) = w(w + 14) + 12 21. x(x - 3) + 4x - 3 = 8x + x(3 + x)

22. -3(x + 5) + x(x - 1) = x(x + 2) - 3 23. n(n - 5) + n(n + 2) = 2n(n - 1) + 1.5

Multiplying Polynomials (pp. 447–452)Lesson 7-7

Find each product.

1. (d + 2)(d + 5) 2. (z + 7)(z - 4) 3. (m - 8)(m - 5)

4. (a + 2)(a - 19) 5. (c + 15)(c - 3) 6. (x + y)(x - 2y)

7. (2x - 5)(x + 6) 8. (7a - 4)(2a - 5) 9. (4x + y)(2x - 3y)

10. (7v + 3)(v + 4) 11. (7s - 8)(3s - 2) 12. (4g + 3h)(2g - 5h)

13. (4a + 3)(2a - 1) 14. (7y - 1)(2y - 3) 15. (2x + 3y)(4x + 2y)

16. (12r - 4s)(5r + 8s) 17. (-a + 1)(-3a - 2) 18. (2n - 4)(-3n - 2)

19. (x - 2)( x 2 + 2x + 4) 20. (3x + 5)(2 x 2 - 5x + 11) 21. (4s + 5)(3 s 2 + 8s - 9)

22. (5x - 2)(-5 x 2 + 2x + 7) 23. (-n + 2)(-2 n 2 + n - 1) 24. ( x 2 - 7x + 4)(2 x 2 - 3x -6)

25. ( x 2 + x + 1)( x 2 - x - 1) 26. ( a 2 + 2a + 5)( a 2 - 3a - 7) 27. (5 x 4 - 2 x 2 + 1)( x 2 - 5x + 3)

Extr

a Pr

actic

e

832 Extra Practice

Special Products (pp. 453–458)Lesson 7-8

Find each product.

1. (t + 7) 2 2. (w - 12)(w + 12) 3. (q - 4h) 2

4. (10x + 11y)(10x - 11y) 5. (4p + 3)2 6. (2b - 4d)(2b + 4d)

7. (a + 2b) 2 8. (3x + y) 2 9. (6m + 2n) 2

10. (3m - 7d) 2 11. (5b - 6)(5b + 6) 12. (1 + x) 2

13. (5x - 9y) 2 14. (8a - 2b)(8a + 2b) 15. (

1 _

4 x + 4

)

2

16. (

1 _

2 x - 10

)

(

1 _ 2 x + 10

)

17. (

1 _ 3 n - m

)

(

1 _ 3 n + m

)

18. (a - 1)(a - 1)(a - 1)

19. (x + 2)(x - 2)(2x + 5) 20. (4x - 1)(4x + 1)(x - 4) 21. (x - 5)(x + 5)(x + 4)(x - 4)

22. (a + 1)(a + 1)(a - 1) (a - 1) 23. (n - 1)(n + 1)(n - 1)

24. (2c + 3)(2c + 3)(2c - 3) (2c - 3) 25. (4d + 5g)(4d + 5g)(4d - 5g)(4d - 5g)

Monomials and Factoring (pp. 471–474)Lesson 8-1

Factor each monomial completely.

1. 240mn 2. -64 a 3 b 3. -26x y 2

4. -231x y 2 z 5. 44r s 2 t 3 6. -756 m 2 n 2

Find the GCF of each set of monomials.

7. 16, 60 8. 15, 50 9. 45, 80 10. 29, 58

11. 55, 305 12. 126, 252 13. 128, 245 14. 7 y 2 , 14 y 2

15. 4xy, -6x 16. 35 t 2 , 7t 17. 16p q 2 , 12 p 2 q, 4pq 18. 5, 15, 10

19. 12mn, 10mn, 15mn 20. 14xy, 12y, 20x 21. 26j k 4 , 16j k 3 , 8 j 2

Using the Distributive Property (pp. 476–482)Lesson 8-2

Use the Distributive Property to factor each polynomial.

1. 10 a 2 + 40a 2. 15wx - 35w x 2 3. 27 a 2 b + 9 b 3

4. 11x + 44 x 2 y 5. 16 y 2 + 8y 6. 14m n 2 + 2mn

7. 25 a 2 b 2 + 30a b 3 8. 2m3 n 2 - 16m n 2 + 8mn 9. 2ax + 6xc + ba + 3bc

10. 6mx - 4m + 3rx - 2r 11. 3ax - 6bx + 8b - 4a 12. a 2 - 2ab + a - 2b

13. 8ac - 2ad + 4bc - bd 14. 2 e 2 g + 2fg + 4 e 2 h + 4fh 15. x 2 - xy - xy + y 2

Solve each equation. Check your solutions.

16. a(a - 9) = 0 17. d(d + 11) = 0 18. z(z - 2.5) = 0

19. (2y + 6)(y - 1) = 0 20. (4n - 7)(3n + 2) 21. (a - 1)(a + 1) = 0

22. 10 x 2 - 20x = 0 23. 8 b 2 - 12b = 0 24. 14 d 2 + 49d = 0

25. 15 a 2 = 60a 26. 33 x 2 = -22x 27. 32 x 2 = 16x

Extra Practice

Extra Practice 833

Quadratic Equations: x 2 + bx + c = 0 (pp. 485–491)Lesson 8-3

Factor each trinomial.

1. x 2 - 9x + 14 2. a 2 - 9a - 36 3. x 2 + 2x - 15

4. n 2 - 8n + 15 5. b 2 + 22b + 21 6. c 2 + 2c - 3

7. x 2 - 5x - 24 8. n 2 - 8n + 7 9. m 2 - 10m - 39

10. z 2 + 15z + 36 11. s 2 - 13st - 30 t 2 12. y 2 + 2y - 35

13. r 2 + 3r - 40 14. x 2 + 5x - 6 15. x 2 - 4xy - 5 y 2

16. r 2 + 16r + 63 17. v 2 + 24v - 52 18. k 2 - 27kj - 90 j 2


19. a 2 + 3a - 4 = 0 20. x 2 - 8x - 20 = 0 21. b 2 + 11b + 24 = 0

22. y 2 + y - 42 = 0 23. k 2 + 2k - 24 = 0 24. r 2 - 13r - 48 = 0

25. n 2 - 9n = -18 26. 2z + z 2 = 35 27. -20x + 19 = - x 2

28. 10 + a 2 = -7a 29. z 2 - 57 = 16z 30. x 2 = -14x - 33

Quadratic Equations: ax 2 + bx + c = 0 (pp. 493–498)Lesson 8-4

Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime.

1. 4 a 2 + 4a - 63 2. 3 x 2 - 7x - 6 3. 4 r 2 - 25r + 6

4. 2 z 2 - 11z + 15 5. 3 a 2 - 2a - 21 6. 4 y 2 + 11y + 6

7. 6 n 2 + 7n - 3 8. 5 x 2 - 17x + 14 9. 2 n 2 - 11n + 13

10. 5 a 2 - 3a + 15 11. 18 v 2 + 24v + 12 12. 4 k 2 + 2k - 12

13. 10 x 2 - 20xy + 10 y 2 14. 12 c 2 - 11cd - 5 d 2 15. 30 n 2 - mn - m 2


16. 8 t 2 + 32t + 24 = 0 17. 6 y 2 + 72y + 192 = 0 18. 5 x 2 + 3x - 2 = 0

19. 9 x 2 + 18x - 27 = 0 20. 4 x 2 - 4x - 4 = 4 21. 12 n 2 - 16n - 3 = 0

22. 12 x 2 - x - 35 = 0 23. 18 x 2 + 36x - 14 = 0 24. 15 a 2 + a - 2 = 0

25. 14 b 2 + 7b - 42 = 0 26. 13 r 2 + 21r - 10 = 0 27. 35 y 2 - 60y - 20 = 0

Quadratic Equations: Differences of Squares (pp. 499–504)Lesson 8-5

Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.

1. x 2 - 9 2. a 2 - 64 3. 4 x 2 - 9 y 2 4. 1 - 9 z 2 5. 16 a 2 - 9 b 2 6. 8 x 2 - 12 y 2

7. a 2 - 4 b 2 8. 75 r 2 - 48 9. x 2 - 36 y 2 10. 3 a 2 - 16 11. 9 x 2 - 100 y 2 12. 49 - a 2 b 2

13. 5 a 2 - 48 14. 169 - 16 t 2 15. 8 r 2 - 4 16. -45 m 2 + 5

Solve each equation by factoring. Check your solutions.

17. 4 x 2 = 16 18. 2 x 2 = 50 19. 9 n 2 - 4 = 0 20. a 2 - 25 _

36 = 0 21. 16

_ 9 - b 2 = 0 22. 18 - 1 _

2 x 2 = 0

23. 20 - 5 g 2 = 0 24. 16 - 1 _ 4 p 2 = 0 25.

1 _

4 c 2 - 4 _

9 = 0 26. 2 q 3 - 2q = 0 27. 3 r 3 = 48r 28. 100d - 4 d 3 = 0

Extr

a Pr

actic

e

834 Extra Practice

Quadratic Equations: Perfect Squares (pp. 505–512)Lesson 8-6

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

1. x 2 + 12x + 36 2. n 2 - 13n + 36 3. a 2 + 4a + 4

4. x 2 - 10x - 100 5. 2 n 2 + 17n + 21 6. 4 a 2 - 20a + 25

Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.

7. 3 x 2 - 75 8. 4 p 2 + 12pr + 9 r 2 9. 6 a 2 + 72 10. s 2 + 30s + 225

11. 24 x 2 + 24x + 9 12. 1 - 10z + 25 z 2 13. 28 - 63 b 2 14. 4 c 2 + 2c - 7


15. x 2 + 22x + 121 = 0 16. 343 d 2 = 7 17. (a - 7) 2 = 5

18. c 2 + 10c + 36 = 11 19. 16 s 2 + 81 = 72s 20. 9 p 2 - 42p + 20 = -29

Graphing Quadratic Functions (pp. 525–536)Lesson 9-1

Use a table of values to graph each function. State the domain and range.

1. y = x 2 + 6x + 8 2. y = - x 2 + 3x 3. y = - x 2

Find the vertex, the equation of the axis of symmetry, and the y-intercept.

4. y = - x 2 + 2x - 3 5. y = 3 x 2 + 24x + 80 6. y = x 2 - 4x - 4

7. y = 5 x 2 - 20x + 37 8. y = 3 x 2 + 6x + 3 9. y = 2 x 2 + 12x

10. y = x 2 - 6x + 5 11. y = x 2 + 6x + 9 12. y = - x 2 + 16x - 15

Consider each equation.

a. Determine whether the function has maximum or minimum value.

b. State the maximum or minimum value.

c. What are the domain and range of the function.

13. y = 4 x 2 - 1 14. y = -2 x 2 - 2x + 4 15. y = 6 x 2 - 12x - 4

16. y = - x 2 - 1 17. y = - x 2 + x + 1 18. y = -5 x 2 - 3x + 2

Solving Quadratic Equations by Graphing (pp. 537–543)Lesson 9-2

Solve each equation by graphing.

1. a 2 - 25 = 0 2. n 2 - 8n = 0 3. d 2 + 36 = 0

4. b 2 - 18b + 81 = 0 5. x 2 + 3x + 27 = 0 6. - y 2 - 3y + 10 = 0

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

7. x 2 + 2x - 3 = 0 8. - x 2 + 6x - 5 = 0 9. - a 2 - 2a + 3 = 0

10. 2 r 2 - 8r + 5 = 0 11. -3 x 2 + 6x - 9 = 0 12. c 2 + c = 0

13. 3 t 2 + 2 = 0 14. - b 2 + 5b + 2 = 0 15. 3 x 2 + 7x = 1

Extra Practice

Extra Practice 835

Transformations of Quadratic Functions (pp. 544–551)Lesson 9-3

Describe how the graph of each function is related to the graph of f(x) = x 2 .

1. g(x) = x 2 – 5 2. h(x) = 1 _ 2 x 2 3. h(x) = - x 2 + 5

4. g(x) = x 2 + 9 5. g(x) = -3 x 2 6. h(x) = - x 2 - 6

7. g(x) = 3 _ 4 x 2 + 4 8. h(x) = 1.2 x 2 - 7.5 9. g(x) = -7 - 4 _

3 x 2

List the functions in order from the most compressed to the least compressed graph.

10. g(x) = -2.3 x 2 , h(x) = 2 _ 3 x 2 11. g(x) = 5 x 2 , h(x) = 1 _

2 x 2

12. g(x) = - x 2 , h(x) = 5 _ 3 x 2 , f(x) = -2.5 x 2 13. g(x) = -6 x 2 , h(x) = 2 x 2 , f(x) = 0.4 x 2

Solving Quadratic Equations by Completing the Square (pp. 552–557)Lesson 9-4

Solve each equation by taking the square root of each side. Round to the nearest tenth if necessary.

1. x 2 - 4x + 4 = 9 2. t 2 - 6t + 9 = 16 3. b 2 + 10b + 25 = 11

4. a 2 - 22a + 121 = 3 5. x 2 + 2x + 1 = 81 6. t 2 - 36t + 324 = 85

Find the value of c that makes each trinomial a perfect square.

7. a 2 + 20a + c 8. x 2 + 10x + c 9. t 2 + 12t + c

10. y 2 - 9y + c 11. p 2 - 14p + c 12. b 2 + 13b + c

Solve each equation by completing the square. Round to the nearest tenth if necessary.

13. a 2 - 8a - 84 = 0 14. c 2 + 6 = -5c 15. p 2 - 8p + 5 = 0

16. 2 y 2 + 7y - 4 = 0 17. t 2 + 3t = 40 18. x 2 + 8x - 9 = 0

19. y 2 + 5y - 84 = 0 20. t 2 + 12t + 32 = 0 21. 2x - 3 x 2 = -8

22. 2 y 2 - y - 9 = 0 23. 2 z 2 - 5z - 4 = 0 24. 8 t 2 - 12t - 1 = 0

Solving Quadratic Equations by Using the Quadratic Formula (pp. 558–565)Lesson 9-5

Solve each equation by using the Quadratic Formula. Round to the nearest tenth if necessary.

1. x 2 - 8x - 4 = 0 2. x 2 + 7x - 8 = 0 3. x 2 - 5x + 6 = 0

4. y 2 - 7y - 8 = 0 5. m 2 - 2m = 35 6. 4 n 2 - 20n = 0

7. m 2 + 4m + 2 = 0 8. 2 t 2 - t - 15 = 0 9. 5 t 2 = 125

10. t 2 + 16 = 0 11. -4 x 2 + 8x = -3 12. 3 k 2 + 2 = -8k

13. 8 t 2 + 10t + 3 = 0 14. 3 x 2 - 5 _ 4 x - 1 _

2 = 0 15. -5 b 2 + 3b - 1 = 0

16. n 2 - 3n + 1 = 0 17. 2 z 2 + 5z - 1 = 0 18. 3 h 2 = 27

State the value of the discriminant for each equation. Then determine the number of real solutions of the equation.

19. 3 f 2 + 2f = 6 20. 2 x 2 = 0.7x + 0.3 21. 3 w 2 - 2w + 8 = 0

22. 4 r 2 - 12r + 9 = 0 23. x 2 - 5x = -9 24. 25 t 2 + 30t = -9

Extr

a Pr

actic

e

836 Extra Practice

Exponential Functions (pp. 567–572)Lesson 9-6

Graph each function. State the y-intercept, and state the domain and range. Then use the graph to determine the approximate value of the given expression. Use a calculator to confirm the value.

1. y = 7 x ; 7 1.5 2. (

1 _

3 )

x ;

(

1 _ 3 )

5.6

3. y = (

3 _ 5 )

x ;

(

3 _ 5 )

-4.2

Graph each function. State the y-intercept.

4. y = 3 x + 1 5. y = 2 x - 5 6. y = 2 x + 3 7. y = 3 x + 1

8. y = (

2 _ 3 )

x 9. y = 5

(

2 _ 5 )

x 10. y = 5( 3 x ) 11. y = 4 (5) x

12. y = 2 (5) x + 1 13. y = (

1 _ 2 )

x + 1

14. y = (

1 _ 8 )

x 15. y =

(

3 _ 4 )

x - 2

Determine whether the data in each table display exponential behavior. Explain why or why not.

16. x -1 0 1 2

y -5 -1 3 7

17. x 1 2 3 4

y 25 125 625 3125

Growth and Decay (pp. 573–579)Lesson 9-7

1. FARMING Mr. Rogers purchased a combine for $175,000 for his farming operation. It is expected to depreciate at a rate of 18% per year. What will be the value of the combine in 3 years?

2. REAL ESTATE The Jacksons bought a house for $65,000 in 1992. Houses in the neighborhood have appreciated at the rate of 4.5% a year. How much is the house worth in 2003?

3. POPULATION In 1950, the population of a city was 50,000. Since then, the population has increased by 2.25% per year. If it continues to grow at this rate, what will the population be in 2005?

4. BEARS In a particular state, the population of black bears has been decreasing at the rate of 0.75% per year. In 1990, it was estimated that there were 400 black bears in the state. If the population continues to decline at the same rate, what will the population be in 2010?

5. INVESTMENTS Determine the amount of an investment if $500 is invested at an interest rate of 5.75% compounded monthly for 25 years.

Geometric Sequences as Exponential Functions (pp. 580–585)Lesson 9-8

1. MONEY Marco deposited $8500 in a 4-year certificate of deposit earning 7.25% compounded monthly. Write an equation for the amount of money Marco will have at the end of the four years. Then find the amount.

2. TRANSPORTATION Elise is buying a new car for $21,500. The rate of depreciation on this type of car is 8% per year. Write an equation for the value of the car in 5 years. Then find the value of the car in 5 years.

3. POPULATION In 2000, the town of Belgrade had a population of 3422. For each of the next 8 years, the population increased by 4.9% per year. Find the projected population of Belgrade in 2008.

Extra Practice

Extra Practice 837

Analyzing Functions with Successive Differences (pp. 586–591)Lesson 9-9

Graph each set or ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function.

1. (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1)

2. (-4, -5), (-2, -4), (0, -3), (2, -2), (4, 0)

3. (-3, 1), (-2, 2), (-1, 4), (0, 8), (1, 16)

Determine which model best describes the data. Then write an equation for the function that models the data.

4. x -2 -1 0 1 2

y 1 0.25 0 0.25 1

5. x -1 0 1 2 3

y 2 _ 3 2 6 18 54

6. x -6 -5 -4 -3 -2

y 2 2.5 3 3.5 4

7. COMPUTER GAME Kylie started a game of computer “Tag, You’re It”. She tagged two friends and so there are three players after round 1. Each of them tagged three friends, and so on. The table shows the number of players after the first few rounds. Determine which function best models the number of players and then write a function that models the data.

8. ROCKET The table shows the height of a rocket that is launched from ground level after a period of 4 consecutive seconds. Determine which model best represents the height of the rocket with respect to time. Then write a function that models the data.

Square Root Functions (pp. 605–610)Lesson 10-1

Graph each function. Determine the domain and range of the function.

1. y = √ ��

x - 4 2. y = √ ��

x + 3 - 1 3. y = 1 _ 3 √

�� x + 2

4. y = √ ��

2x + 5 5. y = -

√

�

4x 6. y = 2 √

�

x

7. y = -3 √

�

x 8. y = √

�

x + 5 9. y = √ �

2x - 1

10. y = 5 √

�

x + 1 11. y = √ ��

x + 1 - 2 12. y = 6 - √ ��

x + 3

Simplifying Radical Expressions (pp. 612–617)Lesson 10-2

Simplify.

1. √ �

50 2. √ ��

200 3. √ ��

162 4. √ ��

700

5. √

� 3 _

√ �

5 6.

√ �

72 _

√ �

6 7. √

�

8 _ 7 8. √

�

7 _ 32

9. √

�

5 _ 8 · √

�

2 _ 6 10. √

�

2 _ 3 · √

�

3 _ 2 11. √

�

2x _

30 12.

√

�

50 _

z 2

13. √ �

10 · √ �

20 14. √ �

7 · √ �

3 15. 6 √ �

2 · √ �

3 16. 5 √ �

6 · 2 √ �

3

17. √

��

4 x 4 y 3 18. √

��

200 m 2 y 3 19. √

��

12t s 3 20. √

��

175 a 4 b 6

21. √

�

54 _

g 2 22.

√

��

99 x 3 y 7 23. √

��

32 c 5 _

9 d 2

24. √

��

27 p 4

_ 3 p 2

Round 1 2 3 4 5

Players 3 9 27 81 243

Times(s) 0 1 2 3 4

Height (ft) 0 1.2 4.8 10.8 19.2

Extr

a Pr

actic

e

838 Extra Practice

Operations with Radical Expressions (pp. 619–623)Lesson 10-3

Simplify.

1. 3 √ �

11 + 6 √ �

11 - 2 √ �

11 2. 6 √ �

13 + 7 √ �

13 3. 2 √ �

12 + 5 √ �

3

4. 9 √ �

7 - 4 √ �

2 + 3 √ �

2 5. 3 √ �

5 - 5 √ �

3 6. 4 √ �

8 - 3 √ �

5

7. 2 √ �

27 - 4 √ �

12 8. 8 √ �

32 + 4 √ �

50 9. √

�

45 + 6 √ �

20

10. 2 √ �

63 - 6 √ �

28 + 8 √ �

45 11. 14 √ �

3t + 8 12. 7 √ �

6x - 12 √ �

6x

13. 5 √ �

7 - 3 √ �

28 14. 7 √ �

8 - √ �

18 15. 7 √ �

98 + 5 √ �

32 - 2 √ �

75

16. 4 √ �

6 + 3 √ �

2 - 2 √ �

5 17. -3 √ �

20 + 2 √ �

45 - √ �

7 18. 4 √ �

75 + 6 √ �

27

19. 10 √

�

1 _ 5 - √

� 45 - 12 √

�

5 _ 9 20. √

� 15 - √

�

3 _ 5 21. 3 √

�

1 _ 3 - 9 √

��

1 _ 12

+ √ ��

243

Find each product.

22. √

�

3 ( √ �

5 + 2) 23. √

�

2 ( √ �

2 + 3 √ �

5 )

24. ( √ �

2 + 5) 2 25. (3 - √

� 7 ) (3 + √

� 7 )

26. ( √ �

2 + √ �

3 ) ( √ �

3 + √ �

2 ) 27. (4 √ �

7 + √ �

2 ) ( √ �

3 - 3 √ �

5 )

Radical Equations (pp. 624–628)Lesson 10-4


1. √

�

5x = 5 2. 4 √ �

7 = √

��

-m 3. √

� t - 5 = 0

4. √

�

3b + 2 = 0 5. √

�

x - 3 = 6 6. 5 - √ �

3x = 1

7. 2 + 3 √

�

y = 13 8. √

�

3g = 6 9. √

�

a - 2 = 0

10. √

�

2j - 4 = 8 11. 5 + √

�

x = 9 12. √

��

5y + 4 = 7

13. 7 + √ �

5c = 9 14. 2 √ �

5t = 10 15. √

�

44 = 2 √

�

p

16. 4 √ ��

x - 5 = 15 17. 4 - √ ��

x - 3 = 9 18. √

��

10x2 - 5 = 3x

19. √

��

2a2 - 144 = a 20. √

��

3y + 1 = y - 3 21. √

��

2 x 2 - 12 = x

22. √

��

b 2 + 16 + 2b = 5b 23. √ ��

m + 2 + m = 4 24. √ ��

3 - 2c + 3 = 2c

The Pythagorean Theorem (pp. 630–635)Lesson 10-5

If c is the measure of the hypotenuse of a right triangle, find each missing measure. If necessary, round to the nearest hundredth.

1. b = 20, c = 29, a = ? 2. a = 7, b = 24, c = ? 3. a = 2, b = 6, c = ?

4. b = 10, c = √ ��

200 , a = ? 5. a = 3, c = 3 √ �

2 , b = ? 6. a = 6, c = 14, b = ?

7. a = √ �

11 , c = √ �

47 , b = ? 8. a = √ �

13 , b = 6, c = ? 9. a = √ �

6 , b = 3, c = ?

10. b = √ �

75 , c = 10, a = ? 11. b = 9, c = √ ��

130 , a = ? 12. a = 9, c = 15, b = ?

Determine whether each set of measures can be sides of a right triangle. Then determine whether they form a Pythagorean Triple.

13. (14, 48, 50) 14. (20, 30, 40) 15. (21, 72, 75) 16. (5, 12, √ ��

119 )

17. (15, 39, 36) 18. (10, 12, √ �

22 ) 19. (2, 3, 4) 20. ( √ �

7 , 8, √ �

71 )

Extra Practice

Extra Practice 839

The Distance and Midpoint Formulas (pp. 636–641)Lesson 10-6

Find the distance between each pair of points with the given coordinates.

1. (4, 2), (-2, 10) 2. (-5, 1), (7, 6) 3. (4, -2), (1, 2) 4. (-2, 4), (4, -2)

5. (3, 1), (-2, -1) 6. (-2, 4), (7, -8) 7. (-5, 0), (-9, 6) 8. (5, -1), (5, 13)

9. (3 √ �

2 , 7), (5 √ �

2 , 9) 10. (6, 3), (10, 0) 11. (3, 6), (5, -5) 12. (-4, 2), (5, 4)

Find the possible values of a if the points with the given coordinates are the indicated distance apart.

13. (0, 0), (a, 3); d = 5 14. (2, -1), (-6, a); d = 10 15. (1, 0), (a, 6); d = √ �

61

Similar Triangles (pp. 642–647)Lesson 10-7

Determine whether each pair of triangles is similar. Justify your answer.

1. 75˚

60˚60˚

2. 50˚

52˚78˚ 78˚

3.

60˚

60˚

For each set of measures given, find the measures of the missing sides if �ABC ∼ �DEF.

4. a = 5, d = 10, b = 8, c = 7

5. a = 2, b = 3, c = 4, d = 3

6. a = 6, d = 4.5, e = 7, f = 7.5

7. a = 15, c = 20, b = 18, f = 10

8. f = 17.5, d = 8.5, e = 11, a = 1.7

Trigonometric Ratios (pp. 649–655)Lesson 10-8

Find the values of the three trigonometric ratios for angle X.

1.

36 39

15

2. 8

610

Use a calculator to find the values of each trigonometric ratio to the nearest ten-thousandth.

3. tan 42º 4. sin 19º 5. cos 78º

c a

b

f d

eD F

EA C

B

c a

b

f d

eD F

EA C

B

Extr

a Pr

actic

e

840 Extra Practice

Inverse Variation (pp. 669–676)Lesson 11-1

Graph each variation if y varies inversely as x.

1. y = 10 when x = 7.5 2. y = -5 when x = 3 3. y = -6 when x = -2

4. y = 1 when x = -0.5 5. y = -2.5 when x = 3 6. y = -2 when x = -1

Assume that y varies inversely as x. Write an inverse variation equation that relates x and y. Then graph the equation.

7. If y = 54 when x = 4, find x when y = 27.



10. If y = 8 when x = -8, find y when x = -16.

11. If y = 3 when x = -8, find y when x = 4.

12. If y = 27 when x = 1 _ 3 , find y when x = 3 _

4 .

13. If y = -3 when x = -8, find y when x = 2.

14. If y = -3 when x = -3, find x when y = 4.

15. If y = -7.5 when x = 2.5, find y when x = -2.5.

16. If y = -0.4 when x = -3.2, find x when y = -0.2.

Rational Functions (pp. 677–683)Lesson 11-2

Identify the asymptotes of each rational function.

1. f(x) = 1 _

x + 4 2. f(x) = x - 2

_ x + 3

3. f(x) = x _ x + 2

4. f(x) = 1 _

x -5 5. f(x) = 3x _

x + 1 6. f(x) = x _

x-6

State the excluded value for each function.

7. f(x) = x + 2

_ x + 3

8. y = 5 _ x 9. y = x _ x -5

10. y = 2 _

3x - 3 11. y = x _

2x + 1 12. y = 3

_ x + 2

Simplifying Rational Expressions (pp. 684–691)Lesson 11-3

State the excluded values for each rational expression.

1. x _

x + 1 2.

m _ n 3. c - 2

_ c 2 - 4

4. b 2 - 5b + 6

__ b 2 - 8b + 15

Simplify each expression. State the excluded values of the variables.

5. 13a _ 39 a 2

6. 38 x 2

_ 42xy

7. p + 5

_ 2(p + 5)

8. a + b

_ a 2 - b 2

9. y + 4

_ y 2 - 16

10. c 2 - 4

_ c 2 + 4c + 4

11. a 2 - a _ a - 1

12. x 2 + 4

_ x 4 - 16

13. r 3 - r 2

_ r - 1

14. 4 t 2 - 8

_ 4t - 4

15. 6 y 3 - 12 y 2

_ 12 y 2 - 18

16. 5 x 2 + 10x + 5 __

3 x 2 + 6x + 3

Extra Practice

Extra Practice 841

Multiplying and Dividing Rational Expressions (pp. 692–698)Lesson 11-4

Find each product.

1. a 2 b _ b 2 c

· c _ d 2. 6 a 2 n _

8 n 2 · 12n _

9a 3.

2 a 2 d _ 3bc

· 9 b 2 c _ 16a d 2

4. 10 n 3

_ 6 x 3

· 12 n 2 x 4 _

25 n 2 x 2 5.

6 m 3 n _ 10 a 2

· 4 a 2 m _ 9 n 3

6. 5n - 5

_ 3 · 9

_ n - 1

7. (a - 5)(a + 1)

__ (a + 1)(a + 7)

· (a + 7)(a - 6)

__ (a + 8)(a - 5)

8. x - 1 __

(x + 2)(x - 3) ·

x + 2 __

(x - 3)(x - 1)

9. a 2 _

a - b · 3a - 3b _ a 10.

2a + 4b _

5 · 25

_ 6a + 8b

Find each quotient.

11. 5 m 2 n _ 12 a 2

÷ 30 m 4 _

18an 12.

25 g 7 h _

28 t 3 ÷

5 g 5 h 2 _

42 s 2 t 3 13.

6a + 4b _

36 ÷

3a + 2b _ 45

14. x 2 y

_ 18z

÷ 2yz

_ 3 x 2

15. p 2 _

14q r 3 ÷

2 r 2 p _

7q 16.

5d - f _

5d + f ÷ (25 d 2 - f 2 )

17. t 2 - 2t - 15

_ t - 5

÷ t + 3

_ t + 5

18. 5x + 10

_ x + 2

÷ (x + 2) 19. 3d _

2 d 2 - 3d ÷ 9

_ 2d - 3

Dividing Polynomials (pp. 700–705)Lesson 11-5

Find each quotient.

1. (2 x 2 - 11x - 20) ÷ (2x + 3) 2. ( a 2 + 10a + 21) ÷ (a + 3)

3. ( m 2 + 4m - 5) ÷ (m + 5) 4. ( x 2 - 2x - 35) ÷ (x - 7)

5. ( c 2 + 6c - 27) ÷ (c + 9) 6. ( y 2 - 6y - 25) ÷ (y + 7)

7. (3 t 2 - 14t - 24) ÷ (3t + 4) 8. (2 r 2 - 3r - 35) ÷ (2r + 7)

9. 12 n 2 + 36n + 15

__ 6n + 3

10. 10 x 2 + 29x + 21

__ 5x + 7

11. 4 t 3 + 17 t 2 - 1

__ 4t + 1

12. 2 a 3 + 9 a 2 + 5a - 12

__ a + 3

13. 27 c 2 - 24c + 8

__ 9c - 2

14. 4 b 3 + 7 b 2 - 2b + 4

__ b + 2

Adding and Subtracting Rational Expressions (pp. 706–713)Lesson 11-6

Find each sum.

1. 4 _ z + 3 _ z 2.

a _ 12

+ 2a _ 12

3. 5 _

2t + -7

_ 2t

4. y _

2 +

y _

2

5. s _ 3 + 2s _

7 6.

5 _

2a + -3

_ 6a

7. 6 _

5x + 7

_ 10 x 2

8. 4a _

2a + 6 + 3

_ a + 3

9. 3t + 2

_ 3t - 2

+ t + 2

_ t 2 - 4

10. -3

_ a - 5

+ -6 _

a 2 - 5a

Find each difference.

11. 5x _ 24

- 3x _ 24

12. 7p

_ 3 -

8p _

3 13. 8k _

5m - 3k _

5m 14. 8

_ m - 2

- 6 _

m - 2

15. y _

b + 6 -

2y _

b + 6 16. a + 2

_ 6 -

a + 3 _

6 17. 3z _

7 w 2 - 2z _ w 18. s _

t 2 - r _

3t

19. a _

a 2 - 4 - 4

_ a + 2

20. m _ m - n - 5 _ m 21.

y + 5 _

y - 5 -

2y _

y 2 - 25

Find the LCM for each pair of polynomials.

22. 27 a 2 bc, 36a b 2 c 2 23. 3m - 1, 6m - 2 24. x 2 + 2x + 1, x 2 - 2x - 3

Extr

a Pr

actic

e

842 Extra Practice

Mixed Expressions and Complex Fractions (pp. 714–719)Lesson 11-7

Write each mixed expression as a rational expression.

1. 4 + 2 _ x 2. 8 + 5 _ 3t

3. b + 1 _

2b + 3b

4. 3z + z + 2 _ z 5. 2

_ a - 2

+ a 2 6. 3 r 2 + 4

_ 2r + 1


7. 3 1 _

2 _

4 3 _ 4 8.

x 2

_ y _

y _

x 3 9.

t 4

_ u _

t 3 _

u 2 10.

x - 3

_ x + 1

_

x 2 _

y 2

11. y _

3 + 5 _

6 _

2 + 5 _ y 12.

1 _ x + 1 _ y

_ 1 _ y - 1 _ x

13. t - 2

_ t 2 - 4

_ t 2 + 5t + 6

14. a + 2

_ a + 1

_

a - 3 _

a - 2

Rational Equations (pp. 720–727)Lesson 11-8

Solve each equation. State any extraneous solutions.

1. k _ 6 + 2k _

3 = -

5 _

2 2.

2x _ 7 + 27

_ 10

= 4x _ 5 3.

18 _

b = 3

_ b + 3

4. 3 _

5x + 7 _

2x = 1 5.

2a - 3 _

6 = 2a _

3 + 1 _

2 6.

3x + 2 _ x +

x + 3 _ x = 5

7. 2b - 3

_ 7 - b _

2 =

b + 3 _

14 8.

2y _

y - 4 - 3 _

5 = 3 9.

2t _ t + 3

+ 3 _ t = 2

10. 5x _

x + 1 + 1 _

x = 5 11.

r - 2 _

r + 2 - 2r _

r + 9 = 6 12. m _

m + 1 + 5

_ m - 1

= 1

13. 2x _ x - 3

- 4x _ 3 - x

= 12 14. 14 _

b - 6 = 1 _

2 + 6

_ b - 8

15. a _ 4a + 15

- 3 = -2

16. 5x _ 3x + 10

+ 2x _ x + 5

= 2 17. 2a - 3 _

a - 3 - 2 = 12

_ a + 2

18. z + 3 _

z - 1 +

z + 1 _

z - 3 = 2

Designing a Survey (pp. 739–745)Lesson 12-1

Identify each sample, suggest a population from which it was selected, and state whether it is unbiased (random) or biased. If unbiased, classify the sample as simple, stratified, or systematic. If biased, classify as convenience or voluntary response.

1. The sheriff has heard that many dogs in the county do not have licenses. He checks the licenses of the first ten dogs he encounters.

2. Every fifth car is selected from the assembly line. The cars are also identified by the day of the week during which they were produced.

3. A table is set up outside of a large department store. All people entering the store are given a survey about their preference of brand for blue jeans. As people leave the store, they can return the survey.

4. A community is considering building a new swimming pool. Every twentieth person on a list of residents is contacted for their opinion.

5. A group of custom chopper builders are interested in finding the type of art work people prefer on their bikes. They line up a group of each of their choppers at a show to see which designs people appear to prefer.

Extra Practice

Extra Practice 843

Analyzing Survey Results (pp. 746–755)Lesson 12-2

Tell which measure of center best represents the data. Justify your answer. Then find the measure of center.

1. COMPUTER USAGE To determine if they need to add more computers for internet access at the Grandview Library, the staff kept track of the number of patrons who used the computers each evening between 5PM and 8PM during a two-week period. {32, 12, 45, 38, 26, 29, 31, 22, 40, 20, 24, 27}

2. CHOCOLATE MILK The preschool cafeteria staff wanted to decide if they should continue to order chocolate milk for the children. For two weeks they kept a count of the number of half-pints of chocolate milk requested by the children. {21, 17, 17, 21, 18, 18, 21, 18, 19, 20}

Given the following portion of a survey report, evaluate the validity of the information and conclusion.

3. ONLINE SURVEYS An online survey was conducted by an advertising firm to determine how many potential customers they might reach. The firm sent out 10,000 surveys and received 2,300 online responses. Question: How many hours per week, outside of work time, do you spend on your computer? Results: 0–2, 4%; 3–6, 20%; 7–12, 32%; 13–20, 20%; 21–30, 12%; more than 30, 12%. Conclusion: One-third of all adults spend between 7 and 12 hours each week on their home computers.

Statistics and Parameters (pp. 756–762)Lesson 12-3

Identify the sample and the population for each situation. Then describe the sample statistic and the population parameter.

1. As part of their quality control program, the Venice Pizza Parlor called 125 of its delivery customers to see if they were satisfied with the delivery service. The percentage of those responding YES is calculated.

2. A random stratified sample of 1,200 high school band members from across the country is surveyed about how many hours they spend practicing each week during football season.

Find the mean, variance, and standard deviation of each set of data.

3. {7, 10, 22, 15, 11} 4. {11, 16, 20, 17} 5. {45, 40, 54, 67, 44}

Permutations and Combinations (pp. 764–770)Lesson 12-4

Determine whether each situation involves a permutation or combination. Explain your reasoning.

1. three topping flavors for a sundae from ten topping choices

2. selection and placement of four runners on a relay team from 8 runners

3. five rides to ride at an amusement park with twelve rides

4. first, second, and third place winners for a 10K race

Evaluate each expression.

5. P(5, 2) 6. P(7, 7) 7. C(10, 2) 8. C(6, 5)

Extr

a Pr

actic

e

844 Extra Practice

Probability of Compound Events (pp. 771–778)Lesson 12-5

1. SIBLINGS Perry took a survey of his classmates to see Classmates’ Siblings

Number of Siblings

Number of Classmates

0 3

1 8

2 4

3 5

4 3

5 1

how many siblings each had. The results are in the table.

a. Find the probability that a randomly chosen classmate will have 4 siblings.

b. Find the probability that a randomly chosen classmate will have less than 3 siblings.

2. CARS A customer visiting a new car lot was looking for a convertible. The Buyers Co. lot had 8 black, 6 white, 4 silver, 5 red and 7 green convertibles to consider.

a. Find the probability that a randomly chosen car will be silver.

b. Find the probability that a randomly chosen car will be red or black.

Probability Distributions (pp. 779–786)Lesson 12-6

Toss 4 coins, one at a time, 50 times and record your results.

1. Based on your results, what is the probability that any two coins show tails?

2. Based on your results, what is the probability that the first and fourth coins show heads?

3. What is the theoretical probability that all four coins show heads?

Use the table that shows the results of Number in Household

Number of Households

1 172

2 293

3 482

4 256

5 or more 148

a survey about household occupancy.

4. Find the experimental probability distribution for the number of households of each size.

5. Based on the survey, what is the probability that a person chosen at random lives in a household with five or more people?

6. Based on the survey, what is the probability that a person chosen at random lives in a household with 1 or 2 people?

Probability Simulations (pp. 787–792)Lesson 12-7

Determine whether the events are independent or dependent. Then find the probability.

1. A bag of colored candies contains 12 red, 5 brown, 7 orange, 6 blue, 4 green and 6 purple candies. Alex reaches in the bag and pulls out one piece of candy and then a second piece. What is the probability that the first two choices are blue?

2. Gretchen and her friends are having a sleepover and movie marathon. They have rented four movies: a comedy, a horror movie, a mystery and a romance. What is the probability that they will watch a mystery and then a romance?

3. For a special game, the sides on a number cube are colored red for the odd numbers, 1, 3, and 5, and green for the even numbers, 2, 4 and 6. What is the probability on two rolls of the cube of getting a green side, followed by a 4?

Mixed Problem

Solving

Mixed Problem Solving 845

Mixed Problem Solving

1. GEOMETRY The area of a rectangle is the product of the length � and the width w. (Lesson 1-1)

a. Write an expression for the area of a rectangle.

b. Write an expression in terms of � for the area of a rectangle that is twice as wide as it is long.

w

�

2. SIGNS A restaurant has a cylindrical shaped sign made to look like a bucket of their fried chicken. The volume of a cylinder can be found by the product of the radius squared, the height of the cylinder and π.

a. Write an expression for the volume of a cylinder.

b. Evaluate the volune of the sign if the radius is 3 feet and the height is 6 feet.

c. For a bill board on the freeway, the dimensions of the sign were changed to a 9 foot diameter and a height of 9 feet. Find the volume of the bucket on the billboard.(Lesson 1-2)

3. TRAVEL Ticket prices for an amusement park are shown in the table below. There are two adults and three children in the Careen family. The children’s ages are 11, 8, and 4. (Lesson 1-3)

a. Write an expression for the cost c of the day at the amusement park for the family.

b. Find the cost of the day at the amusement park.

c. What is the cost per day of the vacation if the family stayed three days?

d. What is the cost per day of the vacation if the family stayed seven days?

Length of Vacation 1–Day 3–Day 7–Day

Guests (Ages 10+) $71 $203 $219

Guests (Ages 3–9) $60 $171 $182

4. FOOD The cafeteria has the following menu.

Menu

Items Cost ($)

pizza 2.75

sandwich 1.50

fries 0.75

drink 1.25

Charlie gets lunch for himself and two friends. Charlie wants pizza and a drink. His friends each have a sandwich, fries, and a drink. (Lesson 1-4)

a. Write and evaluate an expression to find the total cost.

b. How much would it cost if Charlie bought the same thing as his friends?

5. DISTANCE In a given amount of time, Jena drove twice as far as Rita. Altogether they drove 120 miles. Find the number of miles driven by Jena. (Lesson 1-5)

6. GRAPH Describe what is happening in the graph. The graph represents Nikki’s trip to the store. (Lesson 1-6)

Time

Distance

7. Is the following relation a function? Explain. (Lesson 1-7)

Domain Range

6

-3-1

01

8. Find a counterexample for the following statement. If you read music, you sing in a choir. (Lesson 1-7)

9. Identify the hypothesis and conclusion of the following statement. Then write the statement in if-then form. Mei and Janel will go to the mall after school. (Lesson 1-7)

Expressions, Equations, and Functions (pp. 2–71)Chapter 1

Mix

ed P

robl

em S

olvi

ng

846 Mixed Problem Solving

1. BABY-SITTING As a part-time job, Andrea babysits. She charges $4 per hour and $5 for gas money. Write an equation that could be used to find how much she will make if she babysits for 4 hours. (Lesson 2-1)

2. WORLD RECORD At 107 inches, Robert Pershing Wadlow was the tallest man to ever live. If the average 15-year-old male is 68 inches tall, write and solve an equation to find the number of inches taller Mr. Wadlow was than the average 15-year-old male. (Lesson 2-1)

3. Three fifths of Marcus’s classmates have brown eyes. There are 18 students who have brown eyes. Determine how many students are in the class. (Lesson 2-2)

4. LOCKER NUMBERS Andy, Kayla, and Samantha have 3 lockers in a row. The lockers are numbered consecutively and the sum of the locker numbers is 756. Write and solve an equation to find all three locker numbers. (Lesson 2-3)

5. BEAD WORK Sarah said, “I counted my beads, and I have three more than 4 times a certain mystery number.” Jasmine had the same amount of beads as Sarah, but said she had 9 less than 5 times the mystery number. They challenged their art teacher to discover the mystery number. (Lesson 2-4)

a. What equation could the art teacher use to find the number?

b. What is the mystery number?

c. How many beads does each girl have?

6. DRIVING A car has an average fuel economy of 23 miles per gallon. The car gets 4 miles per gallon fewer in city driving and 4 miles per gallon more in highway driving. Write and solve an absolute value equation to find the fuel economy of the car in city and highway driving. (Lesson 2-5)

7. LAWN CARE José’s mom tells him she will pay him $20 if he mows the lawn in an hour, plus or minus 15 minutes. If it takes José 73 minutes to mow the lawn, will his mom pay him? Explain your reasoning. (Lesson 2-5)

8. ARCHITECTURE Isaac drew the following floor plan of his room. Write and solve a proportion to find the actual length of his room if the actual width is 12 meters. (Lesson 2-6)

5 cm

4 cm

9. CARS Daniel’s father purchased a vintage car when it was new. He paid $3334. Last year, he sold it for $28,250. (Lesson 2-7)

a. Determine the percent of change to the nearest percent.

b. Is this a percent of increase or decrease? Explain.

10. WEATHER Emily went to Canada for vacation. Listening to the weather report, she heard that the high for the day was going to be 23°C. She remembered that the formula for changing

Fahrenheit to Celsius was C = 5 _ 9 (F - 32) .

(Lesson 2-8)

a. Solve the formula for F.

b. Use the new formula to find that day’s high temperature in degrees Fahrenheit.

c. If the low temperature for the day was 16°C, find the day’s low in °F.

11. TRANSPORTATION Hector rode his bike to Matthew’s house. It took him 10 minutes to ride the 3-mile trip. When it was time to leave, he saw that his tire had gone flat and he would need to walk home. It took him 45 minutes to walk home. What was his average speed for the round trip? Express your answer in miles per hour. (Lesson 2-9)

Linear Equations (pp. 72–149)Chapter 2

Mixed Problem

Solving


1. MOVIES Tickets for the movies cost $5 for students and $8 for adults. The equation 5x + 8y = 80 represents the number of students x and adults y who can attend a movie for $80. (Lesson 3-1)

a. Use the x- and y-intercepts to graph the equation.

b. Describe what these values mean in the context of this situation.

2. FUNDRAISING Shawn’s class is selling candy to raise money for a class trip. They paid $55 for the candy, and they are selling each candy bar for $1.75. The function y = 1.75x - 55 represents their profit y for selling x candy bars. (Lesson 3-2)

a. Find the zero of the function.

b. Describe what the zero means in the context of this situation.

c. Graph the function.

3. PHOTOS The average cost of using an online photo finisher decreased from $0.50 per print to $0.27 per print between 2002 and 2005. Find the average rate of change in the cost. Explain what the rate of change means. (Lesson 3-3)

4. WAGES The weekly salary Enrique earns w varies directly as the hours h that he works. (Lesson 3-4)

a. Write this situation as an equation.

b. Graph the equation if Enrique makes $11.50 an hour.

c. How many hours does Enrique have to work to earn $690?

5. MONEY The table represents Tiffany’s income. (Lesson 3-5)

Hours Worked Income ($)

1 20.50

2 29.00

3 37.50

4 46.00

a. Write an equation for this sequence.

b. Use the equation to find Tiffany’s income if she works 20 hours.

6. SAVINGS Payat has $680 in a savings account. He makes a deposit after he receives each paycheck. After one month he has $758 in the account. The next month the balance is $836. The balance after the third month is $914. (Lesson 3-5)

a. Write a function to represent the arithmetic sequence.

b. Graph the function.

c. How much will Payat have in his savings account at the end of six months?

7. SALES Percy sells cell phones in the mall. In addition to his salary, he receives a bonus for each cell phone that he sells. The table shows the number of phones he sells and the amount of his bonus. (Lesson 3-6)

Number of Phones Bonus Pay ($)

1 65

2 130

3 195

4 260

5 325

a. Graph the data.

b. Write an equation to describe this relationship.

c. Determine the amount of his bonus if Percy sells 10 phones.

8. STRAWBERRIES The table below shows the cost of picking your own strawberries at a local farm. (Lesson 3-6)

Number of Pounds Total Cost ($)

1 1.25

2 2.50

3 3.75

4 5.00

a. Graph the data.

b. Write an equation in function notation to describe this relationship.

c. How much would 6 pounds of strawberries cost if you picked them yourself?

d. How much would 9.5 pounds of strawberries cost if you picked them yourself?

Linear Functions (pp. 150–209)Chapter 3

Mix

ed P

robl

em S

olvi

ng


1. FINANCES Brandon is saving money to purchase a new video game system. He has $94 and plans to save $7 each week for the next several weeks. (Lesson 4-1)

a. Write an equation for the total amount S that he has saved after w weeks.

b. Graph the equation.

c. Find out how much Brandon will have saved after 8 weeks.

2. PHOTOGRAPHY An online photo processing company produces printed and bound photo albums. The standard price for an album includes up to 20 pages. There is a fee for every two additional pages. To make a 30-page book, you pay $29.94. To make a 42-page book, you pay $41.88. (Lesson 4-2)

a. What is the cost for each additional 2 pages?

b. What is the cost of a 20-page book?

3. FITNESS The graph shows the cost of a membership to the local gym. Write an equation in point-slope form to find the total price y for any number of months x. (Lesson 4-3)

900800700600500400300200100

y

2 4 6 8 10 12 14 16 18x

Pric

e ($

)

Number of Months

4. MAPS The map below shows Interstate Highways 80 and 70 through a portion of Wyoming and Colorado. (Lesson 4-4)

y

x

2

4

6

8

10

2 4 6 8

(2, 1)(6, 2)

(1, 9.75)(5, 10)

80

70

a. Find the slope of the lines that approximate the path of each highway.

b. Are the highways parallel?

Linear Functions and Relations (pp. 210–279)Chapter 4

5. PLANETS The table shows the distance between selected planets and the Sun and the diameters of the planets. Draw a scatter plot and determine what relationship exists, if any, in the data. (Lesson 4-5)

PlanetDistance fromSun ( 10 6 mi)

Diameter(mi)

Mercury 36.0 3032

Venus 67.2 7521

Earth 93.0 7926

Mars 141.6 2159

6. ATTENDANCE Rodeo Houston is an event that features rodeo events, a Bar-B-Que competition, concerts by top performers, art auction and contributes scholarships to youth organizations. The attendance for the rodeo championships are listed in the table below.

Year 2002 2004 2006 2008

Attendance 68,266 70,668 72,867 71,165

a. Find an equation for the median-fit line.

b. According to the equation, how many attended the rodeo’s championship in 2009?

7. PARKING Mika was visiting the state library. The fees for parking are shown in the table. (Lesson 4-7)

Time Cost

15 minutes or less free

fi rst hour $0.50

each addtional houror partial hour

additional $1.00

maximum daily rate $5.00

a. Draw a graph that shows the parking fee y for the time spent parked x.

b. If Mika visited the state library for three and a half hours, how much did she pay for parking?

Mixed Problem

Solving


1. SHOPPING Jeff is buying a new car but owes $3000 on his old one. Jeff can spend no more than $18,000 to pay off his old car and buy a new one. (Lesson 5-1)

a. Write an inequality to show how much Jeff can spend on his new car.

b. Solve the inequality.

2. TOMATOES There are more than 10,000 varieties of tomatoes. One seed company produces seed packages for 200 varieties of tomatoes. For how many varieties do they not provide seeds? (Lesson 5-1)

3. SURVEYS Of the students at Davidson High School, fewer than 92 students said they like strawberry ice cream. This is about one sixth of those surveyed. (Lesson 5-2)

a. Write an inequality to represent this situation.

b. How many students were surveyed?

4. ARCHITECTURE The dimensions of Lisle’s room are shown below. If the area of the room is at least 96 square feet, what is the least width the room could have? (Lesson 5-2)

12 ft

a. Define a variable.

b. Write an inequality.

c. Solve the problem.

5. SAVINGS Ramone is raking yards for $22 per yard to earn money for a car. So far he has $2150 saved. The car that Ramone wants to buy costs at least $8290. (Lesson 5-3)

a. Write an inequality to show how many more yards Ramone still needs to rake to earn enough money to buy the car.

b. Solve the inequality.

6. CHARITY Avery High School holds a walk-a-thon each fall to raise money for charity. This year they want to raise at least $375. Each student earns $0.75 for every half mile walked. How many miles will the students need to walk? (Lesson 5-3)

7. SALES A school buys 500 T-shirts. In addition to the price per shirt, there is a $45 set-up fee. The school can afford to spend no more than $2295. (Lesson 5-3)

a. Write an inequality to show the relationship.

b. What must the price be for the school to afford the shirts?

8. FISH TANK The temperature in a fish tank must be at least 77°F and at most 83°F. (Lesson 5-4)

a. Write a compound inequality that describes acceptable temperatures for a fish tank.

b. Graph the inequality.

9. MOVIES A recent survey showed that 73% of young adults had seen a movie recently. The margin of sampling error was within 5 percentage points. Find the range of young adults who saw a movie recently. (Lesson 5-5)

10. SNOW When the temperature in the clouds is 7°F plus or minus 3°F, star-shaped crystals of snow form. At 14°F plus or minus 4°F, plate-shaped crystals are formed. (Lesson 5-5)

a. Find the range of temperature that produces star-shaped crystals.

b. Find the range of temperature that produces plate-shaped crystals.

11. JOBS It takes a librarian 1 minute to renew a library card and 3 minutes to make a new card. Together, she can spend no more than 30 minutes renewing and making cards. Write an inequality to represent this situation, if x is the number of cards she renews and y is the number of new cards she makes. (Lesson 5-6)

12. MOVING A moving company charges $95 an hour and $0.08 per mile. If Brianna has only $500 for moving expenses, can she afford to hire this moving company if it will take 5 hours and the houses are 75 miles apart? (Lesson 5-6)

13. DELIVERIES A delivery truck is transporting the items shown. (Lesson 5-6)

Item Weight (lb)

television 48

computer 21

If the delivery truck has a 2500-pound weight limit, will the truck be able to deliver 30 televisions and 45 computers? Explain.

Linear Inequalities (pp. 280–329)Chapter 5

Mix

ed P

robl

em S

olvi

ng


1. FUNDRAISERS The French Club is selling heart-shaped lollipops to raise money for a trip to Quebec. They paid $20 for the candy mold, and the ingredients for each lollipop cost $0.50. They plan to sell the lollipops for $1.00. (Lesson 6-1)

a. Write an equation for the cost of supplies y for the number of lollipops sold x, and an equation for the income y for the number of lollipops sold x.

b. Graph each equation.

c. How many lollipops do they need to sell before they begin to make a profit?

2. COMPUTER REPAIR An in-home computer repair provider charges $40 per hour for installations and $60 per hour for troubleshooting and repair. Last week the busiest employee worked 40 hours and brought in $2100. How many hours did the employee spend doing each type of service? (Lesson 6-2)

3. TOURS The Snider family and the Rollins family are traveling together on a trip to visit a candy factory. The number of people in each family and the total cost are shown in the table below. Find the adult admission price and the children’s admission price. (Lesson 6-3)

FamilyNumber of Adults

Number ofChildren

TotalCost

Snider 2 3 $58

Rollins 2 1 $38

4. GEOGRAPHY In 2004, the state capital with the smallest population was Montpelier, Vermont. The state capital with the largest population was Phoenix, Arizona. The difference between the two populations was 1,410,006. The population of Phoenix was 3,881 more than 176 times as large as the population of Montpelier. Find the population of each city. (Lesson 6-4)

5. CANOEING A canoe travels 10 miles upstream in 2.5 hours. The return trip takes the canoe 2 hours. Find the rate of the boat in still water and the rate of the current. (Lesson 6-4)

6. FAIR At a county fair, the cost for 4 slices of pizza and 2 orders of French fries is $21.00. The cost of 2 slices of pizza and 3 orders of French fries is $16.50. To find out how much a single slice of pizza and an order of French fries costs, determine the best method to solve the system of equations. Then solve the system. (Lesson 6-5)

7. OFFICE SUPPLIES At a sale, Ricardo bought 24 reams of paper and 4 inkjet cartridges for $320. Britney bought 2 reams of paper and 1 inkjet cartridge for $50. The reams of paper were all the same price and the inkjet cartridges were all the same price. A system of equations can be used to represent this situation. Determine the best method to solve the system of equations. Then solve the system. (Lesson 6-5)

8. ELEVATIONS The highest and lowest elevations for several states are shown in the table below. (Lesson 6-6)

StateHighest

Elevation (ft)Lowest

Elevation (ft)

Alaska 20,320 0

California 14,494 -282

Colorado 14,433 3,315

Hawaii 13,796 0

Louisiana 535 -8

Wyoming 13,804 3,099

a. Write a matrix to organize the given data.

b. What are the dimensions of the matrix?

c. Which state has the highest elevation? the lowest elevation?

9. KENNEDY SPACE CENTER Admission to the Kennedy Space Center for 2 adults and 3 children costs $160. Admission for 5 adults and 2 children is $246. (Lesson 6-7)

a. Write a system of linear equations to model the situation. Let a represent adult admission, and let c represent child admission.

b. Write the augmented matrix.

c. What is the price for adult and child admissions?

Systems of Linear Equations and Inequalities (pp. 330–397)Chapter 6

Mixed Problem

Solving


1. POOLS Find the area of the swimming pool below. (Lesson 7-1)

4x

5xy

2. GARDENING Felipe is planting a flower garden that is shaped like a trapezoid. Use the formula

A = 1 _ 2 h

(

b 1 + b 2 )

to find the area of Felipe’s

garden. (Lesson 7-1)

6a

4a

3a

3. GEOMETRY The area of a rectangle is 36 m 4 n 6 square meters. The length of the rectangle is 6 m 3 n 3 meters. What is the width of the rectangle? (Lesson 7-2)

4. ASTRONOMY The order of magnitude of the mass of Earth is about 10 24 . The order of magnitude of the mass of the Moon is about 10 22 . How many orders of magnitude as big is the Earth as the Moon? (Lesson 7-2)

5. MAMMALS A blue whale has been caught that was 4.2 × 10 5 pounds. The smallest mammal is a bumblebee bat, which is about 0.0044 pound. (Lesson 7-3)

a. Write the whale’s weight in standard form.

b. Write the bat’s weight in scientific notation.

c. How many orders of magnitude as big is a blue whale as a bumblebee bat?

6. GARDENS Megan had a square garden. She expanded this garden by 3 feet in one direction and 5 feet in the other. (Lesson 7-4)

a. Write a polynomial to describe the area of the new garden if the old garden was x feet wide.

b. If the original width was 12 feet, find the area of the new garden.

c. Find the area of the new garden if the original width was 16.

7. GEOMETRY Write a polynomial that represents the area of the figure. (Lesson 7-5)

z

x y

8. GEOMETRY Find the perimeter and area of the rectangle shown below. (Lesson 7-5)

5x2

+ 2x - 2

4x + 3

9. SHOPPING Nicole bought x shirts for $15.00 each, y pairs of pants for $25.72 each, and z belts for $12.53 each. Sales tax on these items was 7%. Write an expression to find the total cost of Nicole’s purchases. (Lesson 7-6)

10. MANUFACTURING A company is designing a box for dry pasta in the shape of a rectangular prism. The length is 2 inches more than twice the width, and the height is 3 inches more than the length. Write an expression for the volume of the box. (Lesson 7-7)

11. GEOMETRY Write an expression for the area of the trapezoid shown. (Lesson 7-11)

x + 3

3x + 5

2x - 3

12. CARPENTRY Miguel’s room is x feet on each side. He adds book shelves that are 2 feet deep to two adjacent walls. (Lesson 7-8)

a. Show how the new area of the floor space can be modeled by the square of a binomial.

b. Find the square of this binomial.

13. TOYS A flying disk shaped like a circle has a radius of x - 4 centimeters. (Lesson 7-8)

a. Write an expression representing the area of the flying disk.

b. If x is 15, what is the area of the flying disk?

Polynomials (pp. 398–467)Chapter 7

Mix

ed P

robl

em S

olvi

ng


1. CANDY Sada was packing candy into gift bags. She has 42 chocolate truffles, 96 pieces of taffy, and 108 jelly beans. Sada wants to package the same number of candies in each bag, and each bag should have every type of candy. (Lesson 8-1)

a. If she puts the greatest possible number of candies in each bag, how many bags can she make?

b. How many pieces of each type of candy will be in each bag?

2. VOLUNTEERING Catalina’s class collected soap, washcloths, and toothbrushes to give to several homeless shelters in the area. The number of each item collected is shown in the table below. (Lesson 8-1)

Item Number

soap 84

washcloth 24

toothbrush 72

a. If she puts the greatest possible number of items in each box, how many boxes can she make?

b. How many of each item will be in each box?

3. SOCCER Jorge is kicking a soccer ball straight up into the air. The height of the ball is described by the equation h = -16 r 2 + 20t, where h is the height of the ball and t is the time in seconds. How long will it take the ball to hit the ground? (Leson 8-2)

4. PHOTOGRAPHY Kelsey has a 4-inch by 6-inch photograph she wants to frame with a mat. The area of the picture and mat is twice as large as the area of the picture itself. If she wants the mat to be the same width on all sides, what are the outside dimensions of the mat? (Lesson 8-3)

4 in.

6 in.

x

x

5. BALLET A ballet dancer is practicing a leap from the stage to an upper deck. If her initial velocity as she leaps is 18 feet per second, how long is she in the air before she lands on the upper deck, 5 feet above the lower deck? (Lesson 8-4)

5 ft

6. GRAPHICS A computer cartoonist uses the equations y = x 2 - 4 and y = 4 - x 2 as the basis for his drawing of a fish. The graphs of the two equations intersect at the roots of the equations. Find the roots. (Lesson 8-5)

y

x

7. STORAGE Chase is building a box for the shelves in his father’s garage. In order to fit the shelves as neatly as possible, the box needs to be 1 inch taller and 5 inches longer than it is wide. (Lesson 8-6)

a. Let w represent the width of the box. Write an expression for each remaining dimensions in terms of w.

b. If the volume of the box is 2112 cubic feet, what are the dimensions of the box?

V = 2112

� w

h

8. RECREATION Danille and Pete make a slingshot to shoot water balloons. If a water balloon shoots up with an initial velocity of 64 feet per second, how long is it until it hits the ground? (Lesson 8-6)

Factoring and Quadratic Equations (pp. 468–521)Chapter 8

Mixed Problem

Solving


1. PHYSICAL SCIENCE A model rocket is launched with a velocity of 64 feet per second. The equation h = -16 t 2 + 64t gives the height of the rocket t seconds after it is launched. (Lesson 9-1)

a. Graph the function.

b. What is the maximum height that the rocket reaches?

c. How many seconds is the rocket in the air?

2. FIREWORKS Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. The equation h (t) = -16 t 2 + 80t models the height h, in feet, of the fireworks after t seconds. Find the highest point reached by the projectile just as it explodes. (Lesson 9-1)

3. BASEBALL The International Space Agency has landed a robotic explorer on a planet. The robot launches a baseball directly upward at 147 ft/s. The equation for the path of the baseball is h = -49 t 2 + 147t, where h is the height of the baseball in feet and t is time in seconds. Assuming no wind, how long will it take for the ball to land on the surface? (Lesson 9-2)

4. DESIGN For a design competition, Maggie dropped a device from the bleachers. The equation of the device’s height in feet h after t second is h = -16 t 2 + 20. Compare the graph of this function with its parent graph. (Lesson 9-3)

5. PHYSICS An object is launched at 17.2 m/s from a 25-meter tall platform. The equation for the object’s height h at time t seconds after launch is h (t) = -4.9 t 2 + 17.2t + 25, where h is in meters. (Lesson 9-4)

a. Graph this equation.

b. When does the object strike the ground?

6. GEOMETRY The area of a square can be tripled by increasing its length by 6 centimeters and increasing its width by 3 centimeters.

x + 3

x + 6

x

x

What is the length of the side of the square? (Lesson 9-4)

7. FENCE Jackie and Ken are building a fence around a rectangular field. They want to enclose an area of 75 square feet. The width should be 3 feet longer than the length of the field. What are the dimensions of the field? Round to the nearest tenth, if necessary. (Lesson 9-5)

8. VOLLEYBALL A volleyball is thrown straight up. The equation that describes its motion is h (t) = -16 t 2 + 48t + 4, where h represents the height in feet and t represents time in seconds. How long will it take for the ball to hit the ground? Round to the nearest hundredth, if necessary. (Lesson 9-5)

9. BIOLOGY The function f (t) = 50 (1.07) t models the growth of a fly population, where f (t) is the number of flies and t is time in days. After three weeks, approximately how many flies are in this population? (Lesson 9-6)

10. INVESTMENT Nicholas invested $2000 with a 5.75% interest rate compounded monthly. How much money will Nicholas have after 5 years? (Lesson 9-7)

11. RESTAURANTS The total restaurant sales in the United States increased at an annual rate of about 5.2% between 1996 and 2004. In 1996, total sales were $310 billion. (Lesson 9-7)

a. Write an equation for the average sales per year t years after 1996.

b. Predict the total restaurant sales in 2012.

12. TENNIS Each year a local country club sponsors a tennis tournament. Play starts with 256 participants. During each round, half of the players are eliminated. How many players remain after 6 rounds? (Lesson 9-8)

13. CAR CLUB The table shows the number of car club members for four consecutive years after it began. (Lesson 9-9)

Time (years) 0 1 2 3 4

Members 10 20 40 80 160

a. Determine which model best represents the data.

b. Write a function that models the data.

c. Predict the number of car club members after 6 years.

Quadratic and Exponential Functions (pp. 522–601)Chapter 9

Mix

ed P

robl

em S

olvi

ng


1. PENDULUMS The period of a pendulum is the time in seconds it takes to swing from one side to the other and back. If the length of the pendulum � is given in meters, the period T is

given by T = 2π

√

�

�

_ g , where g is the gravitational constant, 9.8 meters per second squared. The Foucault Pendulum at the Pantheon in Paris, France, has a length of 67 meters. Find the period of the Foucault Pendulum. (Lesson 10-1)

2. KINETIC ENERGY The speed v of a ball in meters per second can be determined by the equation

v =

√

��

2k _ m , where k is the kinetic energy in Joules and m is the mass of the ball in kilograms. (Lesson 10-2)

a. Simplify the formula if the mass of the ball is 2 kilograms.

b. If the ball is traveling 10 meters per second, what is the kinetic energy of the ball in Joules?

3. WALLPAPER Ruby is designing a wallpaper border using a pattern of two triangles. If the measurements given are in inches, find the exact length of the segment shown. Then find the length to the nearest quarter inch. (Lesson 10-3)

3 3

x in.

3 2

4. SOUND The speed of sound V in meters per second near Earth’s surface is given by V = 20

√ ��

t + 273 , where t is the surface temperature in degrees Celsius. (Lesson 10-3)

a. What is the speed of sound near Earth’s surface at -1°C and at 6°C in simplest form?

b. Approximately how much faster is the speed of sound at 6°C than at -1°C?

5. SKYDIVING The approximate time t in seconds that it takes an object to fall a distance of d feet

is given by t =

√

��

d _ 16

. Suppose a parachutist

falls 13 seconds before the parachute opens. How far does the parachutist fall during this

time period? (Lesson 10-4)

6. DELIVERY Ben and Amado are delivering a freezer. The bank in front of the house is the same height as the back of the truck. They set up their ramp as shown. What is the length of the slanted part of the ramp to the nearest foot? (Lesson 10-5)

6.2 ft

3.5 ft

7. LADDER An 18-foot ladder is leaning against a building. For stability, the base of the ladder must be 3 feet away from the wall. How far up the wall does the ladder reach? (Lesson 10-5)

8. SNOWMOBILES Tai went snowmobiling with friends. His starting and ending points are shown on the graph. Use the Distance Formula to find how far he has to ride if he can ride straight home. (Lesson 10-6)

(5, 6)

(1, 1)

y

x

9. FLAGS Sarah needs to determine the height of the flag pole in her yard. On a sunny afternoon, Sarah’s shadow is 2 feet 6 inches long. She is 5 feet 3 inches tall. The shadow of the tree is 6 feet long. How tall is the flag pole to the nearest tenth of a foot? (Lesson 10-7)

10. SCHOOL For a class project, Hailey needs to measure the height of her school. Hailey places a mirror 75 feet from the base of the school and backs 10 feet away from the mirror. If Hailey is 5 feet tall, how tall is the school? (Lesson 10-7)

11. LIGHTHOUSE A buoy sits in an ocean 25 feet away from a lighthouse. If the angle formed from the ocean to the top of the lighthouse is 79°, how tall is the lighthouse? (Lesson 10-8)

Radical Functions and Geometry (pp. 602–665)Chapter 10

Mixed Problem

Solving


1. GEOMETRY The length of a rectangle with a constant area is inversely proportional to its width. A rectangle has a length of 10 inches and a width of 6 inches. Another rectangle, has the same area as the first rectangle, but its width is 3 inches. Find the length of the second rectangle. (Lesson 11-1)

2. PHYSICS Given a constant force, the acceleration of an object varies inversely with its mass. A shot putter uses a constant force to put a mass of 8 pounds with an acceleration of 10 feet per second squared. If the shot putter uses the same force on a 16-pound mass, what would be the acceleration? (Lesson 11-1)

3. PHYSICS A rectangle has an area of 36 square

feet. The function � = 36 _ w shows the

relationship between the length and width of the rectangle. Graph the function. (Lesson 11-2)

4. RUNNING A runner runs 12 miles each morning. Her average speed y is given by

y = 12 _ x , where x is the time it takes her to run

12 miles. (Lesson 11-2)

a. Graph the function.

b. Describe the asymptotes.

5. PAINTING The area of each wall in Isabel’s room can be expressed as 2 x 2 + 5x + 3 square feet. A gallon of paint will cover an area that can be expressed as x 2 - 3x - 4 square feet. Write an expression that gives the number of gallons of paint that Isabel will need to buy to paint her room. (Lesson 11-3)

6. TORTOISE A giant tortoise can travel 0.17 mile per hour. What is this speed in feet per minute? (Lesson 11-4)

7. EXCHANGE RATE A pair of shoes bought in France cost 125 euros. The exchange rate at the time was 1 U. S. dollar = 0.68 euro. How much did the shoes cost in U. S. dollars? (Lesson 11-4)

8. GAS A motorcycle travels 225 kilometers with 5 liters of gas. How many liters of gas are needed to travel 135 kilometers? (Lesson 11-4)

9. HOUSING The total cost per month for a dorm is $2250 split equally among 15 students. If 10 more students join the dorm and each pays the same rate as each of the original 15 students, what will be the monthly expenditure? (Lesson 11-4)

10. GEOMETRY The area of a rectangle is 3 x 2 - 6x - 24 square units. What is the length? (Lesson 11-5)

A = 3x2

- 6x - 24 x - 4

11. GARDENING Trey planted a triangular garden. Write an expression for the perimeter of the triangle. (Lesson 11-6)

2a + 6a + 1

3a + 1a + 1

6aa + 1

12. TRACK Trina walked 7 times around the track at a rate of t laps per hour. She ran around the track 10 times at a rate of 4t laps per hour. Write and simplify an expression for the total time it took her to go around the track 17 times. (Lesson 11-6)

13. PLAY A total of 1374 people attended three plays. Let p be the number of people who attended the third play. There were twice as many people at the second play than the third and three times as many people at the first play than the third. Write an expression to represent the fraction of people who attended the first and second plays. (Lesson 11-6)

14. READING Garcia reads 11 1 _ 2 pages of a book in

8 minutes. What is his average reading rate in pages per minute? (Lesson 11-7)

15. RACING A drag racer drove 1 _ 4 mile in about

11 3 _ 4 seconds. What is the speed in miles per

hour? (Lesson 11-7)

16. CAR REPAIR Jack and Ivan are working on Ivan’s car. Jack can complete the job in 6 hours, but Ivan will take 8 hours. They work together for two hours and Jack has to go. How long will it take Ivan to finish his car? (Lesson 11-8)

Rational Functions and Equations (pp. 666–735)Chapter 11

Mix

ed P

robl

em S

olvi

ng


1. CANDY Alicia asked every fourth student that came in the classroom to choose their favorite from three types of candy. (Lesson 12-1)

a. Identify the sample, and suggest a population from which it was selected.

b. Classify the type of data collection used.

c. Identify the sample as biased or unbiased. Explain your reasoning.

d. Classify the sample as simple, stratified, or systematic. Explain your reasoning.

2. HOUSING A listing was made of the rents paid for apartments in a particular neighborhood: {$450, $590, $650, $520, $480, $800, $720, $1600, $600}. Which measure of central tendency best represents the data? Justify your selection, and then find the measure. (Lesson 12-2)

3. CLUBS Given the following portion of a survey report, evaluate the validity of the information and conclusion. (Lesson 12-2)

Question: Should the media club meet before or after school?

Sample: Students were randomly given an invitation to vote while waiting in the school commons for school to start.

Results: 68% before school, 24% after school, 8% no preference

Conclusion: The media club should meet before school.

4. GRADES Lynette took 5 tests in life science this grading period. Find the mean, variance, and standard deviation of the grades she earned: {76, 88, 82, 91, 78}. (Lesson 12-3)

5. FOOTBALL The following table shows information about the number of carries a running back had over a number of years. Find the mean absolute deviation of the number of carries. (Lesson 12-3)

YearNumber of

CarriesYards

per Carry Yards Touchdowns

2002 40 3.7 148 0

2003 90 4.2 378 2

2004 105 4 420 3

2005 115 3.3 379.5 7

2006 140 4.3 602 9

6. BAND In a high school band, six girls and four boys play trumpets. Before auditions at the beginning of the year, the new band director randomly assigns chairs to the students. (Lesson 12-4)

a. How many ways can the band director assign first chair, second chair, and third chair?

b. What is the probability that the first three chairs will be assigned to boys?

7. CARDS If you have drawn and kept the 8 of spades and the 7 of hearts from a standard deck of cards, what is the chance you will draw another 7 or a spade next? (Lesson 12-5)

8. COOKING Nate has a shelf with 3 cans of green beans, 2 cans of corn, and 5 cans of peas and a shelf of 1 package each of egg noodles, rice and ziti. In the freezer, he has 2 pounds of chicken and 3 pounds of beef. If he randomly grabs one item from each area to put in a casserole, what is the probability that he makes a chicken-corn-ziti casserole? (Lesson 12-5)

9. COATS The table shows the probability distribution of the number of each type of coat that was sold in a particular week at a sports store. (Lesson 12-6)

Types of Coats Sold

X = Number of Zippered Pockets

Probability

0 0.03

1 0.08

2 0.08

3 0.10

4 0.30

5 0.41

a. Show that the distribution is valid.

b. What is the probability that a randomly chosen coat has fewer than 4 pockets?

c. Make probability histogram of the data.

10. BASKETBALL Liam plays basketball. Last year, she made 80% of her attempted free throws. What objects can be used to model the possible outcomes of her next free throw? Explain. (Lesson 12-7)

Probability and Statistics (pp. 736–801)Chapter 12

Concepts and Skills Bank

Concepts and Skills Bank 857


1 Converting Units of MeasureThere are three types of measurement: length, capacity, and mass. There are two measuring systems that we use: customary and metric.

The general rule when converting between units of measurement is:

• to convert from larger units to smaller units, multiply;

• to convert from smaller units to larger units, divide.

The diagram below shows the relationship between metric units of length

× 10 × 10 × 10 × 10 × 10 × 10

kilo hector deca METER deci centi milli

÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10

Units of Length

Customary Metric

1 foot (ft) = 12 inches (in.)1 yard (yd) = 3 feet1 mile(mi) = 1760 yards or 5280 feet

1 kilometer (km) = 1000 meters (m)1 meter (m) = 100 centimeters (cm)1 centimeter (cm) = 1 millimeter (mm)

Comparing Metric and Customary Units of Length

Conversion Factors Examples

1 millimeter (mm) ≈ 0.04 inch (in.)1 centimeter (cm) ≈ 0.4 inch (in.)1 meter (m) ≈ 1.1 yards or 3.3 feet (ft)1 kilometer (km) ≈ 0.6 mile (mi)

height of a commahalf the width of a pennywidth of a doorwaylength of a city block

EXAMPLE 1 Units of Length

Complete each sentence.

1A. 5 m =

? cm

5(100) = 500 To convert from meters to centimeters, multiply by 100.5 m = 500 cm

1B. 63 m =

? km

63 ÷ 1000 = 0.063 To convert from meters to kilometers, divide by 1000.63 m = 0.063 km

Units of Capacity

Customary Metric

1 cup (c) = 8 fl uid ounces (fl oz)1 pint (pt) = 2 cups (c)1 quart (qt) = 2 pints (pt)1 gallon (gal) = 4 quarts

1 liter (L) = 1000 milliliters (mL)

Comparing Metric and Customary Units of Capacity


1 milliliter (mL) ≈ 0.03 fl uid ounce (fl oz)1 liter (L) ≈ 1 quart (qt)

drop of waterbottle of ketchup

HS-M-S-SM2 Students will apply to both real

world and mathematical situations US Customary and metric systems of measurement. Also addresses HS-M-S-MPA1, HS-M-S-SM1, and HS-M-S-SM5.

KYPS

Conc

epts

and

Ski

lls B

ank

858 Concepts and Skills Bank

EXAMPLE 2 Units of Capacity


2A. 8 gal =

? quarts

8(4) = 32 Larger smaller, multiply.

8 gal = 32 qt

2C. 16 pt =

? gal

16 ÷ 2 = 8 qt Convert from pt to qt.

8 ÷ 4 = 2 gal Convert from qt to gal

16 pt = 2 gal

Customary Units of Weight Metric Units of Weight

1 pound (lb) = 16 ounces (oz)1 ton (T) = 2000 pounds (lb)

1 kilogram (kg) = 1000 grams (g)1 gram (g) = 1000 milligrams (mg)

Comparing Metric and Customary Units of Mass


1 gram (g) = 0.04 ounce (oz)1 kilogram (kg) = 2.2 pounds (lb)

one raisina pineapple

EXAMPLE 3 Units of Mass


3A. 6.8 kg =

? lb

6.8(2.2) = 14.96 Larger smaller, multiply.

6.8 kg = 14.96 lb

3C. 1T =

? kg

1(2000) = 2000 lb Convert from T to lb.

2000 ÷ 2.2 ≈ 909.1 kg Convert from lb to kg.

1T ≈ 909 kg

Exercises


1. 5 km = ? m 2. 3.5 cm = ? mm 3. 6L = ? mL

4. 37 c = ? pt 5. 0.2 mi = ? ft 6. 400 yd = ? ft

7. 18 cm = ? in. 8. 0.75 L = ? qt 9. 93.5 lb = ? kg

10. 210 mm = ? cm 11. 65 g = ? kg 12. 20 mL = ? L

13. 52.9 kg = ? lb 14. 800 fl oz = ? mL 15. 9.05 yd = ? m

3B. 1.6 oz =

? g

1.6 ÷ 0.04 = 40 Smaller larger, divide.

1.6 oz = 40 g

2B. 24 fl oz =

? c

24 ÷ 8 = 3 Smaller larger, divide.

24 fl oz = 3 c



2 Factors and MultiplesTwo or more numbers that are multiplied to form a product are called factors.

For example, because 6(7) = 42, 6 and 7 are factors of 42.

Factor Rules

This number is a factor of… Example Reason

2 if the ones digit is divisible by 2. 164 4 is divisible by 2.

3 if the sum of the digits is divisible by 3. 123 1 + 2 + 3 = 6, and 6 is divisible by 3.

5 if the ones digit is 0 or 5. 120 The ones digit is a 0.

6 if the number is divisible by 2 and 3. 48 48 is divisible by 2 and 3.

9 if the sum of the digits is divisible by 9. 189 1 + 8 + 9 = 18, and 18 is divisible by 9.

10 if the ones digit is 0. 1250 The ones digit is 0.

EXAMPLE 1

Determine whether 138 has a factor of 2, 3, 5, 6, 9, or 10.

Number Factor? Reason

2 yes 8 is divisible by 2.

3 yes 1 + 3 + 8 = 12, and 12 is divisible by 3.

5 no The ones digit is not 0 or 5.

6 yes 138 has a factor of 2 and 3.

9 no 1 + 3 + 8 = 12, and 12 is not divisible by 9.

10 no The ones digit is not 0.

So, 138 has factors of 2, 3, and 6.

You can also use the factor rules to find all of the factors of a number. Use division to find the other factor in each factor pair.

EXAMPLE 2

List all of the factors of 72.

Number Factor? Factor Pairs

1 yes 1 · 72

2 yes 2 · 36

3 yes 3 · 24

4 yes 4 · 18

5 no …

6 yes 6 · 12

7 no …

8 yes 8 · 9

9 yes 9 · 8

You can stop finding factors when the numbers start repeating.

So, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

A multiple is the product of a specific number and any whole number. So, 64 is a multiple of 4 because 4(16) = 64.

Conc

epts

and

Ski

lls B

ank


EXAMPLE 3

Determine whether 375 is a multiple of 15.

We can use the factor rules to help determine multiples. Since 15 = 3(5), check 3 and 5.

Number Factor of 375? Factor Pairs Is 375 a Multiple?

3 yes 3 · 125 Yes, 375 is a multiple of 3.



Since 375 ÷ 15 = 25 with no remainder, 375 is a multiple of 15.

Exercises

Determine whether each number has a factor of 2, 3, 5, 6, 9, or 10.

1. 39 2. 46 3. 35

4. 18 5. 44 6. 23

7. 22 8. 66 9. 212

10. 250 11. 118 12. 378

13. 995 14. 510 15. 5010

16. 1052 17. 32,460 18. 3039

List all of the factors of each number.

19. 28 20. 75 21. 14 22. 57

23. 81 24. 52 25. 42 26. 63

27. 60 28. 90 29. 114 30. 124

31. 102 32. 135 33. 365 34. 225

Determine whether the first number is a multiple of the second.

35. 49, 3 36. 64, 9 37. 63, 3

38. 60, 6 39. 135, 5 40. 102, 4

41. 121, 11 42. 905, 12 43. 364, 9

44. 536, 3 45. 657, 7 46. 234, 6

47. 282, 31 48. 3612, 12 49. 3585, 65

50. MUSIC Seventy-two members of the marching band will march in the Homecoming Parade. They will need to march in rows with the same number of students in each row.

a. Can the band be arranged in rows of 7? Explain.

b. How many different ways could the marching band members be arranged? Describe the arrangements.

51. CALENDARS Years that are multiples of 4, called leap years, are 366 days long. Use the rule given below to determine whether 2010, 2015, 2016, 2022, and 2032 are leap years.

If the last two digits form a number divisible by 4, then the number is divisible by 4.



3 Prime FactorizationA prime number is a whole number greater than 1, for which the only factors are 1 and itself. A whole number greater than 1 that has more than two factors is a composite number. The numbers 0 and 1 are neither prime nor composite. Notice that 0 has an endless number of factors and 1 has only one factor, itself.

EXAMPLE 1 Identify Numbers as Prime or Composite

Determine whether each number is prime or composite.

a. 27

The numbers 1, 3, and 9 divide into 27 evenly. So, 27 is a composite number.

b. 41

The only numbers that divide evenly into 41 are 1 and 41. So, 41 is a prime number.

A whole number expressed as the product of prime factors is called the prime factorization. The prime factors can be written in any order usually from the least prime factor to the greatest prime factor. Disregarding order, there is only one way to write the prime factorization of a whole number.

EXAMPLE 2 Prime Factorization of a Whole Number

Write the prime factorization of 120.

Method 1 Find the least prime factors.

120 = 2 · 60 The least prime factor of 120 is 2.= 2 · 2 · 30 The least prime factor of 60 is 2.= 2 · 2 · 2 · 15 The least prime factor of 30 is 2.= 2 · 2 · 2 · 3 · 5 The least prime factor of 15 is 3.

Method 2 Use a factor tree.

Choose any two factors of 120 to begin.Keep finding factors until each branch ends in a prime factor.

The prime factorization is complete because 2, 3, and 5 are prime numbers. Thus, the prime factorization of 120 is 2 · 2 · 2 · 3 · 5 or 23 · 3 · 5.

Exercises

Determine whether each number is prime or composite.

1. 48 2. 29 3. 63 4. 75 5. 71 6. 43

Write the prime factorization of each number. Use exponents for repeated factors.

7. 20 8. 28 9. 64

10. 120 11. 140 12. 85

13. 144 14. 221 15. 84

16. 275 17. 210 18. 441

19. 351 20. 900 21. 1350

Conc

epts

and

Ski

lls B

ank


4 Measuring AnglesThe most common measure of angles is the degree (°). You can use a protractor to measure angles in degrees.

EXAMPLE 1

Use a protractor to measure ∠ABC.

Step 1 Place the center point of the protractor’s base on vertex B. Align the straight side with the side

−−

AB so that the marker for 0° is on the side.

Step 2 Use the scale that begins with 0° at −−

AB . Read where the other side of the angle, −−

BC , crosses this scale.

120°

The measure of ∠ABC is 120°. Use the symbols m∠ABC = 120°.

If the sides of the angle are too small to reach the scale on the protractor, you can extend the sides until they are long enough.

Notice that there are measurements going in two directions on the protractor.One is on the outside of the other. You may use either scale for measuring, but you must use the one where one of your sides lines up with 0° to get thecorrect measurement.

Acute angles have measures less than 90°.

Right angles have measures equal to 90°.

Obtuse angles have measures between 90° and 180°.

Straight angles have measures equal to 180°.

So we can classify ∠ABC as an obtuse angle.

A protractor can also be used to draw an angle of a certain measure.

EXAMPLE 2

Draw ∠D with a measure of 85°.

Step 1 Draw a ray with an endpoint D. Make sure that the ray is long enough so that it crosses the edge of the protractor.

Step 2 Place the center point of the protractor on D. Align the mark labeled 0 with the ray you drew.

Step 3 Use the scale that begins with 0. Locate the mark labeled 85. Then draw the other side of the angle.

We can classify this angle as an acute angle.



Exercises

Use the protractor to find the measure of each angle. Then classify each angle as acute, right, obtuse, or straight.

1. ∠JLK 2. ∠ELF

3. ∠ELK 4. ∠GLJ

5. ∠FLI 6. ∠JLF

7. ∠GLF 8. ∠ILG

9. ∠ILK 10. ∠GLK

11. Does ∠FLI have the same measure as ∠ELH? Explain.

12. Which angle, if any, has the same measure as ∠ELH? Explain.

Use a protractor to measure each angle. Then classify each angle as acute, right, obtuse, or straight.

13. 14.

15. 16.

17. 18.

19. 20.

Use a protractor to draw an angle with each measurement. Then classify each angle.

21. 40° 22. 70° 23. 65°

24. 85° 25. 95° 26. 110°

27. 155° 28. 140° 29. 35°

30. 180° 31. 20° 32. 165°

Conc

epts

and

Ski

lls B

ank


5 Venn DiagramsA Venn diagram shows the relationships among sets of numbers or objects by using overlapping circles in a rectangle.

The Venn diagram at the right shows the factors of 12 and 20. The common factors are in both circles.

EXAMPLE 1

COLLEGE Members of a senior class were polled and asked what type of federal financial aid they are receiving for college.

a. How many students are only receiving grants?

The number only in the grant circle is 36. So, 36 seniors are receiving only grants.

b. How many students are receiving both loans and grants?

The value in both circles is 61. So, 61 seniors are receiving both loans and grants.

c. How many students are not receiving any grants or loans?

The value outside of the circles is 15. So, 15 seniors are not receiving any grants or loans.

EXAMPLE 2

Refer to the Venn diagram at the right. Factors of 54

Factors of 45

Factors of 36a. What are the factors in all three circles?

The factors in all three circles are 1, 3, and 9.

b. What is the greatest common factor of all three numbers?

The greatest common factor of all three numbers is 9.

c. What factors are shared only by 54 and 36?

The factors 2, 6, 18 are shared only by 54 and 36.

d. What is the greatest common factor of 54 and 36?

The greatest common factor between 54 and 36 is 18.

e. What factors are shared only by 54 and 45?

There are no factors shared by only 54 and 45. The factors that they have in common are shared by all three numbers.

f. What is the greatest common factor of 54 and 45?

The greatest common factor between 54 and 45 is 9.

LoansGrants

Factors of 20Factors of 12



Exercises

Refer to the Venn diagram at the right.

1. Which factors are in both circles?

2. What is the greatest common factor of 56 and 32?

Refer to the Venn diagram at the right.

3. What are the factors in all three circles?

4. What is the greatest common factor of all three numbers?

5. What factors are shared only by 28 and 42?


7. What factors are shared only by 16 and 42?


TRANSPORTATION Twenty people who have traveled across the country in the last year were asked if they used land or air transportation. The results are shown in the Venn diagram.

9. How many people traveled across the country by land?

10. Explain what the 5 in the diagram represents.

SPORTS Ten students were asked which sports they played in the past month. Use the Venn diagram shown at the right to answer the following questions.

11. Which student(s) have played basketball in the last month?

12. Who played only basketball and baseball?

13. Which student(s) have played only soccer in the last month?

14. Who played only soccer and baseball?

15. Which student(s) have played all three sports?

16. Who played at least two of the three sports?

17. What sports did Ted participate in the past month?

MEDIA A hundred teens were polled and asked which of three news sources they use daily. The results are shown in the Venn Diagram at the right.

18. How many teens use only television as a daily news source?

19. How many teens use television as a daily news source?

20. Which news source(s) was used by exactly 6 teens?

21. How many teens use only the Internet as a daily news source?

22. Which new source(s) was used by exactly 7 teens?

23. How many teens use all three as daily news sources?

AirLand

BaseballSoccer

Basketball

TelevisionNewspapers

Internet



Factors of 42

Conc

epts

and

Ski

lls B

ank


6 Misleading GraphsThe graphs below show the monthly sales of a local magazine.

y

x

Sale

s (th

ousa

nds

$)

MonthF A J A S O N DJ M M J

0

201816141210

8642

Graph AMonthly Sales

y

x

Sale

s (th

ousa

nds

$)Month

F A J A S O N DJ M M J0

1514.5

1413.5

1312.5

1211.5

1110.5

10

Graph BMonthly Sales

The graphs show the same information. However, while the first graph shows fairly steady sales, the second graph shows dramatic increases and decreases in sales. The graphs have the same horizontal axis, but notice that the scales are very different on the vertical axis. By changing the scale on a graph, the visual impression can be changed so that it is misleading.

EXAMPLE 1

The graphs show the number of visitors at a lodge in the Smoky Mountains each year. Which graph appears to show the greatest increase in the number of visitors?

8000

7000

6000

5000

4000

3000

2000

1000

0

Year

Visi

tors

Annual Number of VisitorsAnnual Number of Visitors

1 2 3 4

8000

7500

7000

6500

6000

5500

5000

Year

Visi

tors

Annual Number of VisitorsAnnual Number of Visitors

1 2 3 4

The graph on the right appears to show the greatest growth. The increments are 500 on the vertical axis, rather than 1000 like the first graph. The vertical axis of the graph on the left begins at 0, while the vertical axis of the graph on the right begins at 5000.

More Hints:

• Be sure that both axes have a scale that remains the same throughout the graph.

• Make sure that graphs with pictures, use the same picture throughout the graph.

HS-DAP-S-DR7 Students will identify

and explain misleading uses of data displays. Also addresses HS-DAP-S-CDS13.

KYPS



Exercises

1. TRAFFIC The graphs display the number of cars that went through a tollbooth during the previous hour. Which graph appears to show the greatest increase in the number of vehicles? Explain.

y

x

Num

ber o

f Veh

icle

s

Hour1 3 5 7 82 4 6

0

350325300275250225200175150125100

755025

Tollbooth Traffic

y

x

Num

ber o

f Veh

icle

sHour

1 3 5 7 82 4 6

350

300

250

200

150

100

Tollbooth Traffic

2. Which graph appears to have higher gas prices? Explain.

$3.00

$2.50

$2.00

$1.50

$1.00

$0.50

$0.00

Year

Pric

e Pe

r Gal

lon

($)

Gasoline PricesGasoline Prices

2000 2001 2002 2003 2004 2005 2006

$3.00

$2.75

$2.50

$2.25

$2.00

$1.75

$1.50

$1.25

$1.00

Year

Pric

e Pe

r Gal

lon

($)

Gasoline PricesGasoline Prices

2000 2001 2002 2003 2004 2005 2006

3. BUSINESS According to the information in the graph below, there were no visitors to the ski resort in 1999. Determine if this statement is accurate. Justify your response.

y

x

Visi

tors

Year19

9820

0020

0220

0420

06

4000

3600

3200

2800

2400

2000

Ski Resort Visitors

student handbook - menifee county › userfiles › 27 › classes › 343 › student...

Documents