Q: If $$A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 0 \\ 4 & 2 \end{bmatrix}$$, what is $$A + B$$?

$$\begin{bmatrix} 3 & 1 \\ 4 & 5 \end{bmatrix}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 2

A company models its revenue $$R (in $$thousands of dollars) as a function of time $$t (in $$years) by $$R(t) = 50e$$^{0.03t}$$. What is the revenue after 10 years, rounded to the nearest thousand dollars?

Accepted Answer

$$R(10) \approx 67$$

Question 3

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

Accepted Answer

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

Question 4

Solve the system of equations using matrices:

$$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 5

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 6

If $$f(x) = x^2$ - 4x + 3$$ and $$g(x) = 2x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (2x - 1)^2$ - 4(2x - 1) + 3$$

Question 7

Which of the following is a solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7$$ and $$x = -2$$

Question 8

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 9

Which of the following is the solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 10

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

Accepted Answer

$$x 
eq 2$$

Question 11

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 12

If $$f(x) = x^2$ and g(x) = x + 1$, what is f(g(2$$))$$?

Accepted Answer

$$9$$

Question 13

Which of the following is the sum of the first 5 terms of the arithmetic sequence with $$a_1 = 3$ and d = 4$?

Accepted Answer

$$35$$

Question 14

Solve for $$x$$: $$\log_2$(x) = 5.$$

Accepted Answer

$$x = 32$$

Question 15

Which of the following is the correct solution to the quadratic equation $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 16

A car rental company charges a flat fee of $$\20$ plus $$\$$0.15$$ per mile driven. Which function models the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C(m) = 20 + 0.15m$$

Question 17

Which of the following is the solution to the system of equations $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3,\ y = 2$$

Question 18

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 19

If $$A = \begin{bmatrix} 2 & 1 \ 0 & 3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 0 \ 4 & 2 \end{bmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{bmatrix} 3 & 1 \ 4 & 5 \end{bmatrix}$$

Question 20

Which of the following is the sum of the infinite geometric series $$\sum_{n=0}^{\infty} 5 \left(\frac{1}{2}\right)^n$$?

Accepted Answer

$$10$$

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