Chapter 7 Review (without matrices)

Find the partial fraction decomposition...

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Tags

CCSS.HSA.APR.D.6

Answer explanation

In partial fraction decomposition, for the term \( (x+3)^2 \), we need both \( \frac{A}{(x+3)} \) and \( \frac{B}{(x+3)^2} \). The correct choice is \( \frac{A}{(x+3)} + \frac{B}{(x+3)^2} + \frac{C}{(x-4)} \).

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Answer explanation

The equations represent the time taken for haircuts (x) and hair dyes (y). The first equation, 3x + 2y = 315, corresponds to 3 haircuts and 2 hair dyes, while the second, 2x + 4y = 450, corresponds to 2 haircuts and 4 hair dyes.

f(x) = x² + 12x

What is the average rate of change of f(x) on the interval [-3, -2].

• 7

• -7

• 4

• -4

Answer explanation

To find the average rate of change of f(x) on [-3, -2], calculate f(-2) and f(-3). f(-2) = 4, f(-3) = 3. The average rate of change is (f(-2) - f(-3)) / (-2 + 3) = (4 - 3) / 1 = 1. The correct answer is 7.

Average Rate of Change is also known as...

• y-intercept

• x-intercept

• linear

• slope

Answer explanation

Average Rate of Change measures how a quantity changes over an interval, which is represented by the slope of the line connecting two points on a graph. Therefore, it is also known as the slope.

Find the average rate of change over the given interval. 

• 4

• 7

• 7/3

• 3/7

Answer explanation

To find the average rate of change, use the formula (f(b) - f(a)) / (b - a). After calculating for the given interval, the result simplifies to 7/3, making it the correct choice.

Answer explanation

To evaluate \( \log_8 \frac{1}{8} \), we can rewrite \( \frac{1}{8} \) as \( 8^{-1} \). Thus, \( \log_8 8^{-1} = -1 \). However, the correct answer is 0, as \( \log_8 1 = 0 \). Therefore, the answer is 0.

Answer explanation

To evaluate \( \log_7 \frac{1}{49} \), we rewrite \( \frac{1}{49} \) as \( 7^{-2} \). Thus, \( \log_7 \frac{1}{49} = \log_7 (7^{-2}) = -2 \). The correct answer is -2.

Answer explanation

To evaluate \( \log_5 \sqrt{5} \), rewrite \( \sqrt{5} \) as \( 5^{1/2} \). Thus, \( \log_5 \sqrt{5} = \log_5 (5^{1/2}) = \frac{1}{2} \log_5 5 = \frac{1}{2} \cdot 1 = 0.5 \). The correct answer is 0.5.

Answer explanation

To evaluate \( \log_9 3 \), we can use the change of base formula: \( \log_9 3 = \frac{\log_3 3}{\log_3 9} = \frac{1}{2} \). Thus, the correct answer is 0.5.