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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 11 A1 Glencoe Algebra 1

Chapter Resources

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME

DATE PERIOD

Chapter 11 3 Glencoe Algebra 1Anticipation GuideRational Expressions and Equations

Before you begin Chapter 11

• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 11

• Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.11

Step 1STEP 1

A, D, or NSStatementSTEP 2

A or D

1. Since a direct variation can be written as y = kx, an inverse

variation can be written as y = x ? k . D

2. A rational expression is an algebraic fraction that contains

a radical. D

3. To multiply two rational expressions, such as 2xy2

3c and 3 c 2 5y multiply the numerators and the denominators. A

4. When solving problems involving units of measure,

dimensional analysis is the process of determining the units of the final answer so that the units can be ignored while performing calculations. D

5. To divide (4x2 + 12x) by 2x, divide 4x2 by 2x and 12x by 2x.

A

6. To find the sum of 2a

(3a - 4) and 5 (3a - 4) , first add the numerators and then the denominators. D

7. The least common denominator of two rational expressions

will be the least common multiple of the denominators. A

8. A complex fraction contains a fraction in its numerator

or denominator. A

9. The fraction

(a ? b ) ( c ? d ) can be rewritten as ac bd D

10. Extraneous solutions are solutions that can be eliminated

because they are extremely high or low. D

Step 2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME

DATE PERIOD

Lesson 11-1

Chapter 11 5 Glencoe Algebra 1Both methods show that x2 = 8 ? 3 when y = 18.

Exercises

Determine whether each table or equation represents an inverse or a direct variation. Explain. 1. x y 3 6 5 10 8 16

12 24 2. y = 6x 3. xy = 15

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

4. If y = 10 when x = 5, 5. If y = 8 when x = -2,

find y when x = 2. xy = 50; 25 find y when x = 4. xy = -16; -4

6. If y = 100 when x = 120, 7. If y = -16 when x = 4,

find x when y = 20. xy = 12,000; 600 find x when y = 32. xy = -64;-2

8. If y = -7.5 when x = 25, find y when x = 5.

xy = -187.5; -37.5

9. DRIVING The Gerardi family can travel to Oshkosh, Wisconsin, from Chicago, Illinois,

in 4 hours if they drive an average of 45 miles per hour. How long would it take them if they increased their average speed to 50 miles per hour? 3.6 h

10. GEOMETRY For a rectangle with given area, the width of the rectangle varies inversely

as the length. If the width of the rectangle is 40 meters when the length is 5 meters, find the width of the rectangle when the length is 20 meters. 10 m

Study Guide and Intervention

Inverse Variation

Identify and Use Inverse Variations An inverse variation is an equation in the

form of y = k ? x or xy = k. If two points (x1, y1) and (x2, y2) are solutions of an inverse variation,

then x1 ∙ y1 = k and x2 ∙ y2 = k. Product Rule f or Inverse Variationx1 ∙ y1 = x2 ∙ y2 From the product rule, you can form the proportion x1 ? x2 = y1 ? y2 . If y varies inversely as x and y = 12 when x = 4, find x when y = 18.

Method 1 Use the product rule.

x1 ∙ y1 = x2 ∙ y2 Product rule for inverse variation 4 ∙ 12 = x2 ∙ 18 x1 = 4, y1 = 12, y2 = 18 48
18 = x

2 Divide each side by 18.

8 ? 3 = x

2 Simplify.Method 2 Use a proportion.

x 1 ? x 2 = y 2 ? y 1

Proportion for inverse variation

4 ? x 2 = 18 12 x1 = 4, y1 = 12, y2 = 18

48 = 18x2 Cross multiply.

8 ? 3 = x2 Simplify.11-1

Example

direct variation; of the form y = kxdirect variation; of the form y = kxinverse variation; of the form xy = k

Answers (Anticipation Guide and Lesson 11-1)

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 11 A2 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME

DATE PERIOD

Chapter 11 6 Glencoe Algebra 1Study Guide and Intervention (continued)

Inverse Variation

Graph Inverse Variations Situations in which the values of y decrease as the values of x increase are examples of inverse variation. We say that y varies inversely as x, or y is inversely proportional to x.

Suppose you drive

200 miles without stopping. The time

it takes to travel a distance varies inversely as the rate at which you travel. Let x = speed in miles per hour and y = time in hours. Graph the variation.

The equation xy = 200 can be used to

represent the situation. Use various speeds to make a table. xy O 20 40
60
30
20 10

Graph an inverse

variation in which y varies inversely as x and y = 3 when x = 12.

Solve for k.

xy = k Inverse variation equation

12(3) = k x = 12 and y = 3

36 = k Simplify.

Choose values for x and y, which have a

product of 36. xy O 12 24
24
12

Exercises

Graph each variation if y varies inversely as x.

1. y = 9 when x = -3 2. y = 12 when x = 4 3. y = -25 when x = 5

xy O 24
12 -12 -24 -12 -24 12 24 x y O3216 -16 -32 -16-32 16 32 xy O

50-50-100 100100

50
-50 -100

4. y = 4 when x = 5 5. y = -18 when x = -9 6. y = 4.8 when x = 5.4

xy O 20 10quotesdbs_dbs31.pdfusesText_37

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