C Challenge

For Exercises 47–49, each expression represents the side length of a cube. Write a polynomial in standard form for the surface area of each cube.

47. x + 2
48. 3a + 1
49. 2 c 2 + 3 2 , c squared , plus 3

50. Financial Planning Suppose you deposit $1500 for college in a savings account that has an annual interest rate r (expressed as a decimal). At the end of 3 years, the value of your account will be 1500 ( 1 + r ) 3 1500 . open 1 plus r close cubed  dollars.

    1. Rewrite the expression 1500 ( 1 + r ) 3 1500 . open 1 plus r close cubed  by finding the product 1500(1 + r)(1 + r)(1 + r). Write your answer in standard form.
    2. How much money is in the account after 3 yr if the interest rate is 3% per year?

Standardized Test Prep

SAT/ACT

51. Which expression is equivalent to ( x + 4 ) ( x − 9 ) ? open x plus 4 close open x minus 9 close question mark

    1. x 2 + 5 x − 36 x squared , plus 5 x minus 36
    2. x 2 − 5 x − 36 x squared , minus 5 x minus 36
    3. x 2 − 13 x − 36 x squared , minus 13 x minus 36
    4. x 2 − 13 x − 5 x squared , minus 13 x minus 5

52. Malia is making a landscape drawing for her backyard. She is drawing a sidewalk. She uses the graph of the equation y = 3 x + 2 y equals 3 x plus 2  to represent one edge of the sidewalk. She wants the other edge of the sidewalk to be parallel to the first edge through the point (3, 4). The graph of which of the following lines represents the other edge of the sidewalk?

    6. y = x + 2 y equals x plus 2
    7. y = 4 x + 2 y equals 4 x plus 2
    8. y = 3 x − 9 y equals 3 x minus 9
    9. y = 3 x − 5 y equals 3 x minus 5

53. What is (are) the solution(s) of the equation | x + 3 | = 7 ? vertical line x plus 3 vertical line equals 7 question mark

    1. 4 and − 10 negative 10
    2. 4 and − 4 negative 4
    3. 4
    4. 10

Extended Response

54. A trapezoid is determined by the following system of inequalities.

    y ≥ 3 y ≤ 9 x ≤ 8 y ≤ 2 x + 3 y greater than or equal to 3 y less than or equal to 9 x less than or equal to 8 y less than or equal to 2 x plus 3

    1. Graph the trapezoid in the coordinate plane.
    2. The formula for the area A of a trapezoid is A =   1 2 ( b 1 + b 2 ) h , eh . equals , 1 half . open , b sub 1 , plus , b sub 2 , close h comma  where b 1 b sub 1  and b 2 b sub 2  are the bases of the trapezoid and h is its height. What is the area of the trapezoid you graphed in part (a)? Show your work.

Mixed Review

See Lesson 8-2.

Factor each polynomial.

55. 6 x − 4 6 x minus 4
56. b 2 + 8 b b squared , plus 8 b
57. 10 t 3 − 25 t 2 + 20 t 10 , t cubed , minus 25 , t squared , plus 20 t

Get Ready! To prepare for Lesson 8-4, do Exercises 58–61.

See Lesson 7-4.

Simplify each expression.

58. ( 6 x ) 2 open , 6 x , close squared
59. ( 2 y ) 2 open , 2 y , close squared
60. ( − 3 m ) 2 open negative 3 m close squared
61. ( − 5 n ) 2 open negative 5 n close squared

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