Q: Which of the following is the correct matrix product for $$\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix} \times \begin{pmatrix}2 & 0\\1 & 2\end{pmatrix}$$?

$$\begin{pmatrix}4 & 4\\10 & 8\end{pmatrix}$$

Question 1

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 2

A biologist is modeling the population of a bacteria culture with the function $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1.5}$$ \approx 2241$$

Question 3

Which of the following is the correct graph for the function $$f(x) = -2x + 4$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$4$$

Question 4

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -5x^2$ + 40x$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$R(5) = 100 at$$ $$x = 5$$

Question 5

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 6

Which of the following expressions is equivalent to $$\log_{2}(8x)$$?

Accepted Answer

$$3 + \log$$_{2}$$x$$

Question 7

A medication’s concentration in the bloodstream is modeled by $$C(t) = 20e$$^{-0.2t}$$, where t$ is in hours. After how many hours will the concentration drop to 5$ mg/L?

Accepted Answer

$$t = 6.93$$

Question 8

Which of the following is the correct solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 9

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

Accepted Answer

$$x 
eq 3$$

Question 10

A savings account earns interest compounded annually at a rate of $$4\%. If $$you deposit $$\1000$, how much will you have after 3 years? (Use A = P(1 + r)^t$)

Accepted Answer

$$A = 1000(1.04)^3$ \approx 1124.86$$

Question 11

Which of the following is the correct matrix product for $$\begin{pmatrix}1 & 2\3 & 4\end{pmatrix} 	imes \begin{pmatrix}2 & 0\1 & 2\end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix}4 & 4\10 & 8\end{pmatrix}$$

Question 12

Which of the following is the correct solution to the equation $$\dfrac{3}{x} + 2 = 5$$?

Accepted Answer

$$x = 3$$

Question 13

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 21.9$$ meters

Question 14

Which of the following is the correct inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+7}{3}$$

Question 15

A car’s value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 4 years?

Accepted Answer

$$V(4) = 20000(0.85)^4$ \approx 10441$$

Question 16

Which of the following is the correct solution to the equation $$\ln(x) = 2$$?

Accepted Answer

$$x = e^2$

Question 17

A business uses the function $$C(x) = 1000 + 5x to $$model its costs, where $$x is $$the number of units produced. If the business sells each unit for $$15$$, what is the minimum number of units it must sell to break even?

Accepted Answer

$$x = 100$$

Question 18

Which of the following is the correct solution to the equation $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 19

Which of the following is the sum of the geometric series $$2 + 6 + 18 + 54$$?

Accepted Answer

$$80$$

Question 20

A patient’s temperature $$T (in$$ $$^\circF) is $$modeled by $$T(t) = 98.6 + 1.5\sin(\frac{\pi}{12}t)$$, where $$t is $$hours after midnight. What is the maximum temperature during the day?

Accepted Answer

$$100.1^\circF$$

College Algebra with Corequisite Support – Course Syllabus and Study Guide

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