Question 1

Solve for $$x in $$the equation $$8(5x+6) = 11 - (x+7). $$What is the solution?

Accepted Answer

$$x = -\dfrac{44}{41}$$

Question 2

Which of the following values cannot be a solution to the rational equation $$\dfrac{6}{3x+4} - \dfrac{1}{x-7} = 0$$?

Accepted Answer

$$x = -\dfrac{4}{3}$$

Question 3

Solve the quadratic equation $$w^2 - 13w + 40 = 0$ by factoring. What are the solutions?

Accepted Answer

$$w = 8,\ 5$$

Question 4

A company models its annual revenue with the function $$f(t) = 2282e$$^{0.0241t}$$, where t$ is the number of years since 2000. In what year did the revenue reach 3615$ dollars per household?

Accepted Answer

2019

Question 5

Given $$f(x) = \dfrac{x-5}{x-8}$$, what are the vertical and horizontal asymptotes?

Accepted Answer

Vertical: $$x=8$$, Horizontal: $$y=1$$

Question 6

Solve the logarithmic equation $$\log_{16} \sqrt[3]{13} = x. $$What is $$x$$?

Accepted Answer

$$x = \dfrac{1}{6}$$

Question 7

Find the equation of the line that passes through $$(-2,4)$$ and has a slope of $$-9.$$

Accepted Answer

$$9x + y = 63$$

Question 8

Given $$f(x) = 5x^2$ - 3x + 2$$, what is the vertex of the parabola?

Accepted Answer

$$\left(\dfrac{3}{10},\ \dfrac{31}{20}\right)$$

Question 9

Solve for $$x in $$the equation $$\ln(5x) = 5.2. $$Give your answer in exact form.

Accepted Answer

$$x = \dfrac{e$$^{5.2}$$}{5}$$

Question 10

Given $$f(x) = x^3$ - 6x^2$ + 3x + 10$$ and that $$2 is a $$zero, what are all the zeros of $$f(x)$$?

Accepted Answer

$$x = -1,\ 2,\ 5$$

Question 11

Solve the rational equation $$\dfrac{2x+3}{2} - \dfrac{3x}{x-4} = x. $$What is the solution?

Accepted Answer

$$x = -4$$

Question 12

Which of the following is the equation of the horizontal line passing through $$(-2,4)$$?

Accepted Answer

$$y = 4$$

Question 13

Given $$f(x) = \dfrac{(x+2)(x-3)}{x+1}$$, what is the vertical asymptote?

Accepted Answer

$$x = -1$$

Question 14

Solve the quadratic equation $$2y^2 + 5y = -3$ by factoring. What are the solutions?

Accepted Answer

$$y = -1,\ -\dfrac{3}{2}$$

Question 15

Solve the logarithmic equation $$\log_3$(x^3 - 18) = 2$. What is x$?

Accepted Answer

$$x = 3$$

Question 16

Given $$f(x) = x^3$ + 6x^2$ + 3x - 10$$ and that $$-5 is a $$zero, what are all the zeros of $$f(x)$$?

Accepted Answer

$$x = 1,\ -2,\ -5$$

Question 17

Find the equation of the line passing through $$(-2,4)$$ and $$(6,5).$$

Accepted Answer

$$x - 8y = -34$$

Question 18

Solve the equation $$\dfrac{1}{x-3} + \dfrac{1}{x+4} = \dfrac{1}{x^2$ + x - 12}. $$Which values cannot be solutions?

Accepted Answer

$$x = 3,\ -4$$

Question 19

Solve the equation $$\log_5$\left(\dfrac{1}{25}\right) = 2x. $$What is $$x$$?

Accepted Answer

$$x = -1$$

Question 20

Given $$f(x) = x^3$ + 7x^2$ + 4x - 12$$ and that $$-6 is a $$zero, what are all the zeros of $$f(x)$$?

Accepted Answer

$$x = 1,\ -2,\ -6$$

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