C Challenge

56. Simplify ( a + b + c ) 2 . open eh plus b plus c close squared . .

57. Number Theory You can use factoring to show that the sum of two multiples of 3 is also a multiple of 3.

    If m and n are integers, then 3m and 3n are multiples of three. 3 m + 3 n = 3 ( m + n ) 3 m plus 3 n equals 3 open m plus n close

    Since m + n is an integer, 3(m + n) is a multiple of three.

    1. Show that if an integer is one more than a multiple of 3, then its square is also one more than a multiple of 3.
    2. Reasoning If an integer is two more than a multiple of 3, is its square also two more than a multiple of 3? Explain.
58. The formula V = 4 3 π r 3 v equals , 4 thirds , pi , r cubed  gives the volume of a sphere with radius r. Find the volume of a sphere with radius x + 3. Write your answer in standard form.

Standardized Test Prep

SAT/ACT

59. What is a simpler form of ( 2 x + 5 ) ( 2 x − 5 ) ? open 2 x plus 5 close open 2 x minus 5 close question mark

    1. 4 x 2 − 20 x − 25 4 , x squared , minus 20 x minus 25
    2. 4 x 2 + 20 x + 25 4 , x squared , plus 20 x plus 25
    3. 4 x 2 − 25 4 , x squared , minus 25
    4. 2 x 2 − 5 2 , x squared , minus 5

60. Sara and Nick sold tickets to a play. Sara sold 20 student tickets and 3 adult tickets for more than $60. Nick sold 15 student tickets and 5 adult tickets for less than $75. This information can be represented by 20 x + 3 y > 60 20 x plus 3 y greater than 60  and 15 x + 5 y < 75 , 15 x plus 5 y less than 75 comma  where x is the price of a student ticket and y is the price of an adult ticket. The inequalities are graphed below. Which could be the price of a student ticket?

    
    Image Long Description

    Ticket Sales

    6. $1
    7. $2.75
    8. $5.50
    9. $6

Short Responce

61. Graph the solutions of the system.

    5 x + 4 y ≥ 20 5 x plus 4 y greater than or equal to 20

    5 x + 4 y ≤ 20 5 x plus 4 y less than or equal to 20

Mixed Review

See Lesson 8-3.

Simplify each product.

62. ( 3 x + 2 ) ( 2 x − 5 ) open 3 x plus 2 close open 2 x minus 5 close
63. ( 4 m − 1 ) ( 6 m − 7 ) open 4 m minus 1 close open 6 m minus 7 close
64. ( x + 9 ) ( 5 x + 8 ) open x plus 9 close open 5 x plus 8 close

See Lesson 2-10.

Find each percent change. Describe the percent change as an increase or decrease. If necessary, round to the nearest tenth.

65. $ 4  to  $ 3 dollars 4 , to , dollars 3
66. 4 ft to 5 ft
67. 12 lb to 15 lb
68. $ 40  to  $ 35 dollars 40 , to , dollars 35

Get Ready! To prepare for Lesson 8-5, do Exercises 69–71.

See Lesson 8-2.

Factor each polynomial.

69. 12 x 4 + 30 x 3 + 42 x 12 , x to the fourth , plus 30 , x cubed , plus 42 x
70. 72 x 3 + 54 x 2 + 27 72 , x cubed , plus 54 , x squared , plus 27
71. 35 x 3 + 7 x 2 + 63 x 35 , x cubed , plus 7 , x squared , plus 63 x

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