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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 .

2. A rational expression is an algebraic fraction that contains

a radical.

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

and 3 c 2 multiply the numerators and the denominators.

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.

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

6. To find the sum of 2a

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

7. The least common denominator of two rational expressions

will be the least common multiple of the denominators.

8. A complex fraction contains a fraction in its numerator

or denominator.

9. The fraction

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

10. Extraneous solutions are solutions that can be eliminated

because they are extremely high or low.

Step 2

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

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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. x y

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 ? 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 ∙ 12 = x2 ∙ 18 x1 = 4, y1 = 12, y2 = 18 = x

2 Divide each side by 18.

8 ? 3 = x

2 Simplify.Method 2 Use a proportion.

? x = y ? y

Proportion for inverse variation

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

48 = 18x2 Cross multiply.

? 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

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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.

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

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