7. A rational expression has one or more fractions in
the numerator and denominator.
ANSWER: false; complex fraction
Study Guide and Review - Chapter 11
State whether each sentence is true or false . If
false , replace the underlined word, phrase,
expression, or number to make a true
sentence.
8. The expression
can be simplified to .
2
1. The least common multiple for x − 25 and x − 5 is x
− 5.
ANSWER: true
ANSWER: 9. A direct variation can be represented by an equation
of the form k = xy, where k is a nonzero constant.
2
false; x − 25
ANSWER: false; inverse variation
2. If the product of two variables is a nonzero constant,
the relationship is an inverse variation.
ANSWER: true
10. The rational function
asymptote at y = 3.
3. If the line x = a is a vertical asymptote of a rational
function, then a is an excluded value.
ANSWER: true
4. A rational expression is a fraction in which the
numerator and denominator are fractions.
has a horizontal ANSWER: true
Solve. Assume that y varies inversely as x.
11. If y = 4 when x = 1, find x when y = 12.
ANSWER: ANSWER: false; polynomials
5. The excluded values for
are −2 and −3.
12. If y = −1 when x = −3, find y when x = −9.
ANSWER: ANSWER: true
6. The equation
has an extraneous 13. If y = 1.5 when x = 6, find y when x = −16.
solution, 2.
ANSWER: ANSWER: true
7. A rational expression has one or more fractions in
the numerator and denominator.
ANSWER: false; complex fraction
14. PHYSICS A 135-pound person sits 5 feet from the
center of a seesaw. How far from the center should
a 108-pound person sit to balance the seesaw?
ANSWER: 6.25 ft or 6 ft 3 in.
State the excluded value for each function.
8. The expression
can be simplified to .
15. ANSWER: eSolutions
true Manual - Powered by Cognero
9. A direct variation can be represented by an equation
ANSWER: 3
Page 1
center of a seesaw. How far from the center should
a 108-pound person sit to balance the seesaw?
ANSWER: Study
Guide and Review - Chapter 11
6.25 ft or 6 ft 3 in.
The vertical asymptote is at x = 0 and the horizontal
asymptote is at y = 0.
State the excluded value for each function.
15. Simplify each expression.
20. ANSWER: 3
ANSWER: 16. 21. ANSWER: ANSWER: 17. 22. ANSWER: 2
ANSWER: 18. ANSWER: −4
23. 19. PIZZA PARTY Katelyn ordered pizza and soda for
her study group for $38. The cost per person y is
given by
ANSWER: , where x is the number of people in
the study group. Graph the function and describe the
asymptotes.
ANSWER: 24. ANSWER: 25. ANSWER: The vertical asymptote is at x = 0 and the horizontal
asymptote is at y = 0.
Simplify each expression.
State the excluded values for each function.
20. 26. ANSWER: eSolutions Manual - Powered by Cognero
ANSWER: −6, −3
Page 2
ANSWER: ANSWER: Study Guide and Review - Chapter 11
State the excluded values for each function.
32. 26. ANSWER: ANSWER: −6, −3
33. GEOMETRY Find the area of the rectangle
shown. Write the answer in simplest form.
27. ANSWER: Find each product or quotient.
28. ANSWER: xy
ANSWER: Find each quotient.
3
2
34. (x − 2x − 22x + 21) ÷ (x − 3)
ANSWER: 29. ANSWER: 3
2
35. (x + 7x + 10x − 6) ÷ (x + 3)
ANSWER: 2
x + 4x − 2
30. 2 2
2
36. (5x y − 10x y + 5xy) ÷ 5xy
ANSWER: ANSWER: xy − 2x + 1
2
37. (48y + 8y + 7) ÷ (12y − 1)
31. 2
÷ (b − 6b + 8)
ANSWER: ANSWER: 2
38. GEOMETRY The area of a rectangle is x + 7x +
13. If the length is (x + 4), what is the width of the
rectangle?
32. ANSWER: ANSWER: eSolutions Manual - Powered by Cognero
33. GEOMETRY Find the area of the rectangle
Find each sum or difference.
39. Page 3
that is
37. (48y + 8y + 7) ÷ (12y − 1)
ANSWER: feet long and wide. What is the perimeter of the room?
ANSWER: 4 ft
Study Guide and Review - Chapter 11
2
38. GEOMETRY The area of a rectangle is x + 7x +
13. If the length is (x + 4), what is the width of the
rectangle?
Simplify each expression.
44. ANSWER: ANSWER: Find each sum or difference.
39. ANSWER: 45. ANSWER: 40. ANSWER: 1
46. 41. ANSWER: ANSWER: (x + 5)(x − 2)
42. 47. ANSWER: ANSWER: 43. DESIGN Miguel is decorating a model of a room
that is
feet long and perimeter of the room?
ANSWER: 4 ft
Simplify each expression.
44. wide. What is the 48. FABRICS Donna makes sets of three different
sized tablecloths to sell. A small one takes one-half
yard of fabric, a medium one takes five-eighths yard,
and a large one takes one and one-quarter yards.
a. How many yards of fabric does she need to make
one set of the three tablecloths? b. If Donna can make a set of tablecloths in 38
minutes, what is the average rate of fabric she uses
in yards per hour? ANSWER: eSolutions Manual - Powered by Cognero
ANSWER: a.
yd
b.
yd/min
Page 4
ANSWER: Study Guide and Review - Chapter 11
48. FABRICS Donna makes sets of three different
sized tablecloths to sell. A small one takes one-half
yard of fabric, a medium one takes five-eighths yard,
and a large one takes one and one-quarter yards.
a. How many yards of fabric does she need to make
one set of the three tablecloths? b. If Donna can make a set of tablecloths in 38
minutes, what is the average rate of fabric she uses
in yards per hour? 53. ANSWER: −2, 4
54. PAINTING Anne can paint a room in 6 hours.
Oljay can paint a room in 4 hours. How long will it
take them to paint the room working together?
ANSWER: ANSWER: a.
yd
b.
yd/min
Solve each equation. State any extraneous
solutions.
49. ANSWER: , extraneous: 2
50. ANSWER: 51. ANSWER: 24
52. ANSWER: no solution
53. ANSWER: −2, 4
54. PAINTING Anne can paint a room in 6 hours.
How long will it
take them to paint the room working together?
eSolutions
Manual
- Powered
by Cognero
Oljay
can paint
a room
in 4 hours.
ANSWER: Page 5