Question 1

A wheelchair manufacturer has a cost function $$C(x) = 250x + 32$$ where $$x is $$the number of wheelchairs produced. What is the average cost function $$\overline{C}(x)$$?

Accepted Answer

$$\overline{C}(x) = \dfrac{250x + 32}{x}$$

Question 2

Acme Car rental charges $$4 per day plus 0.15 $$per mile. Interstate rental charges $$3 per day and 0.05 $$per mile. How many miles must be driven for Acme to be a better deal than Interstate?

Accepted Answer

$$m \u003c 10$$

Question 3

Simplify the rational expression: $$\dfrac{x^2$ - 7x - 15}{x^2$ - 25}$$

Accepted Answer

Question 4

What are the restrictions on the variable for the rational expression $$\dfrac{x-9}{x+1}$$?

Accepted Answer

$$x 
eq -1$$

Question 5

Find the common denominator for $$\dfrac{x+5}{7x^2$+21x}$$ and $$\dfrac{5}{x^2$+6x+9}.$$

Accepted Answer

$$(x+3)^2(7x$$)$$

Question 6

Rewrite $$\sqrt{15ab}$$ using rational exponents.

Accepted Answer

$$(15ab)^{1/2}$$

Question 7

Solve for $$x$$: $$x^3 - 8 = -4$

Accepted Answer

$$x = 2$$

Question 8

Solve for $$h in $$the formula $$A = \dfrac{1}{2}bh.$$

Accepted Answer

$$h = \dfrac{2A}{b}$$

Question 9

Solve and write the solution in interval notation: $$3x - 5 \u003c -20$$

Accepted Answer

$$(-\infty, -5)$$

Question 10

What is the solution set in interval notation for $$|x-1| \leq 3$$?

Accepted Answer

$$[-2, 4]$$

Question 11

Solve for $$x$$: $$2 + \sqrt{2x-1} = x$$

Accepted Answer

$$x = 3$$

Question 12

Simplify using radical notation: $$25^{\frac{3}$${2}}$$

Accepted Answer

$$5^3 = 125$

Question 13

What is the interval notation for the solution to $$1 \leq 2x + 3 \u003c 11$$?

Accepted Answer

$$[-1, 4)$$

Question 14

What is the restriction on $$w$$ for the expression $$\dfrac{w+5}{w^2$-9}$$?

Accepted Answer

$$w 
eq 3$$ and $$w 
eq -3$$

Question 15

Rewrite $$\sqrt[5]{4}$$ using rational exponents.

Accepted Answer

$$4^{1/5}$$

Question 16

Solve for $$r in $$the formula $$A = 4\pi r^2$.

Accepted Answer

$$r = \sqrt{\dfrac{A}{4\pi}}$$

Question 17

What is the solution in interval notation for $$2 - 3x \u003c 8$$?

Accepted Answer

$$(-\infty, -2)$$

Question 18

Simplify $$-32^{\frac{3}$${5}}$$ using radical notation.

Accepted Answer

$$-8$$

Question 19

What is the restriction on $$y$$ for the expression $$\dfrac{7}{y^2$-4}$$?

Accepted Answer

$$y 
eq 2$$ and $$y 
eq -2$$

Question 20

Solve for $$x$$: $$\sqrt{y+1} - 9 = 0$$

Accepted Answer

$$y = 80$$

College Algebra: Rational Expressions, Functions, and Inequalities Study Guide

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