83. Music The pitch, or frequency, of a piano note is related to its position on the keyboard by the function F ( n ) = 440 ⋅ 2 n 12 , f open n close equals 440 dot , 2 super n over 12 end super . comma  where F is the frequency of the sound waves in cycles per second and n is the number of piano keys above or below Concert A, as shown. If n = 0 n equals 0  at Concert A, which of the instruments shown in the diagram can sound notes at the given frequency?

    
    Image Long Description

    1. 590
    2. 120
    3. 1440
    4. 2093

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

84. The graph below shows the translation of the graph of the parent function y = y equals  | x | down 2 units and 3 units to the right. What is the area of the shaded triangle in square units?

    

85. What does x equal if log (1 +3x) = 3?
86. Using the change of base formula, what is the value of x for which log 9 x = log 3 5 ? log base 9 , x equals , log base 3 , 5 question mark
87. The polynomial x 4 + 3 x 3 + 16 x 2 − 19 x + 8 x to the fourth , plus 3 , x cubed , plus , 16 x squared , minus 19 x plus 8  is divided by the binomial x − 1 . x minus 1 .  What is the coefficient of x 2 x squared  in the quotient?
88. What positive value of b makes x 2 + b x + 81 x squared , plus b x plus 81  a perfect square trinomial?

Mixed Review

See Lesson 7-4.

Expand each logarithm.

89. log 2 x 3 y − 2 log . 2 x cubed . y super negative 2 end super
90. log 3 x y log base 3 . x over y
91. log 3 9 x log base 3 . square root of 9 x end root

See Lesson 6-6.

Let f ( x ) = 3 x and g ( x ) = x 2 − 1 . f open x close equals , 3 to the x , and g open x close equals , x squared , minus 1 .  Perform each function operation.

92. ( g − f ) ( x ) open g minus f close open x close
93. ( f ∘ g ) ( x ) open f composition g close open x close
94. ( g ∘ f ) ( x ) open g composition f close open x close

See Lesson 5-6.

Find all the zeros of each function.

95. y = x 3 − x 2 + x − 1 y equals , x cubed , minus , x squared , plus x minus 1
96. f ( x ) = x 4 − 16 f open x close equals , x to the fourth , minus 16
97. f ( x ) = x 4 − 5 x 2 + 6 f open x close equals , x to the fourth , minus , 5 x squared , plus 6

Get Ready! To prepare for Lesson 7-6, do Exercises 98–100.

See Lesson 7-4.

Write each logarithmic expression as a single logarithm.

98. log 2 15 − log 2 5 log base 2 , 15 minus , log base 2 , 5
99. log 3 + 4 log x log 3 plus 4 log x
100. 5 log 7 2 − 2 log 7 y 5 , log base 7 , 2 minus 2 , log base 7 , y

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