glencoe division - perry county middle school · three times its width. ... what are the dimensions...
TRANSCRIPT
![Page 1: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/1.jpg)
Pre-Algebra Interactive Chalkboard
Copyright © by The McGraw-Hill Companies, Inc.
Send all inquiries to:
GLENCOE DIVISION
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, Ohio 43240
![Page 2: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/2.jpg)
![Page 3: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/3.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 4: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/4.jpg)
Lesson 13-1 Polynomials
Lesson 13-2 Adding Polynomials
Lesson 13-3 Subtracting Polynomials
Lesson 13-4 Multiplying a Polynomial by a Monomial
Lesson 13-5 Linear and Nonlinear Functions
Lesson 13-6 Graphing Quadratic and Cubic Functions
![Page 5: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/5.jpg)
Example 1 Classify Polynomials
Example 2 Degree of a Monomial
Example 3 Degree of a Polynomial
Example 4 Degree of a Real-World Polynomial
![Page 6: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/6.jpg)
Determine whether is a polynomial. If it is,
classify it as a monomial, binomial, or trinomial.
Answer: The expression is not a polynomial becausehas a variable in the denominator.
![Page 7: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/7.jpg)
Answer: This is a polynomial because it is the difference of two monomials. There are two terms, so it is a binomial.
Determine whether is a polynomial. If it is, classify it as a monomial, binomial, or trinomial.
![Page 8: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/8.jpg)
Determine whether each expression is a polynomial. If it is, classify it as a monomial, binomial, or trinomial.
a.
b.
Answer: yes; trinomial
Answer: not a polynomial
![Page 9: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/9.jpg)
Answer: The variable w has degree 4, so the degree
of –10w4 is 4.
Find the degree of .
![Page 10: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/10.jpg)
Find the degree of .
has degree 3, has degree 7, and z has degree 1.
Answer: The degree of
![Page 11: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/11.jpg)
Find the degree of each monomial.
a.
b.
Answer: 3
Answer: 8
![Page 12: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/12.jpg)
Find the degree of .
04
7
degreeterm
Answer: The greatest degree is 7. So, the degree of the
polynomial is 7.
![Page 13: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/13.jpg)
Find the degree of .
Answer: The greatest degree is 7. So, the degree of the
polynomial is 7.
7
4
degreeterm
![Page 14: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/14.jpg)
Find the degree of each polynomial.
a.
b.
Answer: 5
Answer: 6
![Page 15: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/15.jpg)
Answer:
Area The formula for the surface area (A) of a cube is , where s is the side length. Find the degree of the polynomial.
![Page 16: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/16.jpg)
Answer: 2
Area The formula for the surface area S of a cylinder with height h and radius r is .Find the degree of the polynomial.
![Page 17: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/17.jpg)
![Page 18: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/18.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 19: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/19.jpg)
Example 1 Add Polynomials
Example 2 Use Polynomials to Solve a Problem
![Page 20: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/20.jpg)
Find .
Method 1 Add vertically.
Method 2 Add horizontally.
Align like terms.
Add.
Associative and Commutative Properties
Answer: The sum is 10w + 1.
![Page 21: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/21.jpg)
Find .
Method 1 Add vertically.
Method 2 Add horizontally.
Align like terms.
Add.
Write the expression.
Group like terms.
Simplify.
Answer: The sum is
![Page 22: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/22.jpg)
Find .
Write the expression.
Simplify.
Answer: The sum is
![Page 23: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/23.jpg)
Find .
Answer: The sum is .
Leave a space because there is no other term like xy.
![Page 24: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/24.jpg)
Find each sum.
a.
b.
c.
d.
Answer:
Answer:
Answer:
Answer:
![Page 25: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/25.jpg)
Geometry The length of a rectangle is
units and the width is 8x – 1 units.
Find the perimeter.
Answer: The perimeter is
Formula for the perimeter of a rectangle
Distributive Property
Simplify.
Group like terms.
Replace with
and w with
![Page 26: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/26.jpg)
Answer: The length of the rectangle is 16 units.
Find the length of the rectangle if
Write the expression.
Replace x with –3.
Simplify.
![Page 27: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/27.jpg)
Geometry The length of a rectangle is
units and the width is 6w – 3 units.
a. Find the perimeter.
b. Find the length if
Answer:
Answer: 39 units
![Page 28: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/28.jpg)
![Page 29: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/29.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 30: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/30.jpg)
Example 1 Subtract Polynomials
Example 2 Subtract Using the Additive Inverse
Example 3 Subtract Polynomials to Solve a Problem
![Page 31: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/31.jpg)
Find .
Answer: The difference is .
Align like terms.
Subtract.
![Page 32: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/32.jpg)
Find .
Subtract.
Answer: The difference is .
Align like terms.
![Page 33: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/33.jpg)
Find each difference.
a.
b.
Answer:
Answer:
![Page 34: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/34.jpg)
Find .
To subtract (3x + 9), add (–3x – 9).
Group the like terms.
Simplify.
Answer: The difference is x–17.
![Page 35: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/35.jpg)
Find .
Align the like terms and add the additive inverse.
Answer:
The additive inverse of
![Page 36: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/36.jpg)
Find each difference.
a.
b.
Answer: 10c – 7.
Answer:
![Page 37: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/37.jpg)
Geometry The length of a rectangle isunits. The width is units. How much longer is the length than the width?
Answer: The length is units longer than the width.
difference in measurement
Add additive inverse.
Group like terms.
Simplify.
Substitution
![Page 38: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/38.jpg)
Profit The ABC Company’s costs are given bywhere x = the number of items produced.
The revenue is given by 5x. Find the profit, which is the difference between the revenue and the cost.
Answer:
![Page 39: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/39.jpg)
![Page 40: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/40.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 41: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/41.jpg)
Example 1 Products of a Monomial and a Polynomial
Example 2 Product of a Monomial and a Polynomial
Example 3 Use a Polynomial to Solve a Problem
![Page 42: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/42.jpg)
Find .
Answer: – 24x – 16
Simplify.
Distributive Property
![Page 43: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/43.jpg)
Find .
Simplify.
Answer:
Distributive Property
![Page 44: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/44.jpg)
Find each product.
a. 3(–5m – 2)
b. (4p – 8)(–3p)
Answer: –15m – 6
Answer:
![Page 45: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/45.jpg)
Find
Distributive Property
Simplify.
Answer:
![Page 46: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/46.jpg)
Find
Answer:
![Page 47: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/47.jpg)
Fences The length of a dog run is 4 feet more than three times its width. The perimeter of the dog run is 56 feet. What are the dimensions of the dog run?
Explore You know the perimeter of the dog run. You want to find the dimensions of the dog run.
Plan Let w represent the width of the dog run.
Then 3w + 4 represents the length. Write an equation.
Perimeter equals twice the sum of the length and width.
P = 2
![Page 48: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/48.jpg)
Solve
Answer: The width of the dog run is 6 feet, and the length is
Write the equation.
Replace P with 56 and
Combine like terms.
Distributive Property
Subtract 8 from each side.
Divide each side by 8.
![Page 49: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/49.jpg)
Examine Check the reasonableness of the results.
The answer checks.
![Page 50: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/50.jpg)
Garden The length of a garden is four more than twice its width. The perimeter of the garden is 44 feet. What are the dimensions of the garden?
Answer: 6 feet by 16 feet
![Page 51: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/51.jpg)
![Page 52: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/52.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 53: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/53.jpg)
Example 1 Identify Functions Using Graphs
Example 2 Identify Functions Using Equations
Example 3 Identify Functions Using Tables
Example 4 Describe a Linear Function
![Page 54: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/54.jpg)
Determine whether the graph represents a linear or nonlinear function.
Answer: The graph is a straight line, so it represents a linear function.
![Page 55: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/55.jpg)
Determine whether the graph represents a linear or nonlinear function.
Answer: The graph is a curve, not a straight line, so it represents a nonlinear function.
![Page 56: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/56.jpg)
Answer: nonlinear Answer: linear
Determine whether each graph represents a linear or nonlinear function.a. b.
![Page 57: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/57.jpg)
Determine whether represents a linear or nonlinear function.
Answer: This equation represents a linear functionbecause it is written in the form
![Page 58: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/58.jpg)
Answer: This equation is nonlinear because x is raised to the second power and the equation cannot be written in the form
Determine whether represents a linear ornonlinear function.
![Page 59: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/59.jpg)
Determine whether each equation represents a linearor nonlinear function.
a.
b.
Answer: nonlinear
Answer: linear
![Page 60: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/60.jpg)
Determine whether the table represents a linear or nonlinear function.
x y
2 25
4 17
6 9
8 1
+2
+2
–8
–8
–8
As x increases by 2, y decreases by 8. So, this is a linear function.
Answer: linear
+2
![Page 61: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/61.jpg)
Determine whether the table represents a linear or nonlinear function.
x y
5 2
8 4
11 8
14 16
+3
+3
+3
+2
+4
+8
As x increases by 3, y increases by a greater amount each time. So, this is a nonlinear function.
Answer: nonlinear
![Page 62: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/62.jpg)
Determine whether each table represents a linear or nonlinear function.
169
137
115
103
yxa. b.
137
108
79
410
yx
Answer: nonlinear Answer: linear
![Page 63: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/63.jpg)
Multiple-Choice Test Item Which rule describes a linear function?
A B C D
Read the Test Item
A rule describes a relationship between variables. A rule that can be written in the form describes a relationship that is linear.
![Page 64: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/64.jpg)
Solve the Test Item
This is a nonlinear function because x is in the
denominator and the equation cannot be written in the form
You can eliminate choices A and D.
This is a quadratic equation. Eliminate choice C.
Answer: The answer is B.
quadratic equation
![Page 65: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/65.jpg)
CheckThis equation is in the form
![Page 66: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/66.jpg)
Answer: C
Multiple-Choice Test ItemWhich rule describes a linear function?
A B C D
![Page 67: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/67.jpg)
![Page 68: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/68.jpg)
Click the mouse button or press the Space Bar to display the answers.
![Page 69: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/69.jpg)
Example 1 Graph Quadratic Functions
Example 2 Use a Function to Solve a Problem
Example 3 Graph Cubic Functions
![Page 70: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/70.jpg)
Answer:
Graph .
(1.5, 4.5)1.5
(1, –2)1
(0, 0)0
(0.5, –0.5)0.5
(–0.5, –0.5)–0.5
(–1, –2)–1
(–1.5, –4.5)–1.5
(x, y)x
Make a table of values, plot the ordered pairs, and connect the points with a curve.
![Page 71: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/71.jpg)
Answer:
Graph .
(2, 3)2
(1, 1.5)1
(0, 1)0
(–1, 1.5)–1
(–2, 3)–2
(x, y)x
![Page 72: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/72.jpg)
Answer:
Graph .
(2, –7)2
(1, –4)1
(0, –3)0
(–1, –4)–1
(–2, 7)–2
(x, y)x
![Page 73: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/73.jpg)
Graph each function.
a.
Answer:
![Page 74: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/74.jpg)
Graph each function.
b.
Answer:
![Page 75: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/75.jpg)
Graph each function.
c.
Answer:
![Page 76: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/76.jpg)
Geometry The height of a triangle is 4 times its base. Write a formula for the area and graph it. Find the area of the triangle whose base is 3 units.
Words The area of a triangle is equal to one-half theproduct of its base and height.
Variables .
Equations Area is equal to one-half the product of its base and height
A =
![Page 77: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/77.jpg)
The equation is . Since the variable b has an
exponent of 2, this function is nonlinear. Now graph .
Since the base cannot be negative, use only positive
values of b.
(2.5, 12.5)2.5
(2, 8)2
(1.5, 4.5)1.5
(1, 2)1
(0.5, 0.5)0.5
(0, 0)0
(b, A)b
![Page 78: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/78.jpg)
By looking at the graph, we find that for a base of 3 units, the area of the triangle is 18 square units.
![Page 79: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/79.jpg)
Geometry The length of a rectangle is 3 times its width. Write a formula for the area and graph it. Find the area of the rectangle whose width is 3.5 inches.
Answer:
![Page 80: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/80.jpg)
Answer:
Graph .
(2, –4)2
(1, – )1
(0, 0)0
(–1, )–1
(–2, 4)–2
(x, y)x
![Page 81: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/81.jpg)
Answer:
Graph .
(1.5, 8.75)1.5
(1, 4)1
(0, 2)0
(–1, 0)–1
(–1.5, –4.75)–1.5
(x, y)x
![Page 82: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/82.jpg)
Answer:
Graph each function.
a.
![Page 83: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/83.jpg)
Graph each function.
b.
Answer:
![Page 84: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/84.jpg)
![Page 85: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/85.jpg)
Explore online information about the information introduced in this chapter.
Click on the Connect button to launch your browser and go to the Pre-Algebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.pre-alg.com/extra_examples.
![Page 86: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/86.jpg)
End of Custom Shows
WARNING! Do Not RemoveThis slide is intentionally blank and is set to auto-advance to end
custom shows and return to the main presentation.
![Page 87: GLENCOE DIVISION - Perry County Middle School · three times its width. ... What are the dimensions of the dog run? Explore You know the ... the area of the rectangle whose width](https://reader034.vdocument.in/reader034/viewer/2022051801/5ae1f2a67f8b9a5d648c08a7/html5/thumbnails/87.jpg)