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

$$\begin{bmatrix} 3 & 2 \\ 4 & 6 \end{bmatrix}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) by $$P(t) = 5e$$^{0.2t}$$. What type of function is this, and what does the base of the exponent represent in this context?

Accepted Answer

Exponential; the base $$e$$ represents continuous growth.

Question 3

Solve the equation $$2x^2 - 8x + 6 = 0$ for x$.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 6

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

Question 7

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(1, 2)$$

Question 8

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 9

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

Accepted Answer

$$f(g(2)) = (2 + 1)^2$ = 9$$

Question 10

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

Accepted Answer

$$h = 21.9$$ meters

Question 11

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 12

Which of the following describes the graph of $$y = |x - 3| + 2$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 2)$$

Question 13

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

Accepted Answer

$$80$$

Question 14

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

Accepted Answer

$$\begin{bmatrix} 3 & 2 \ 4 & 6 \end{bmatrix}$$

Question 15

Which of the following is the correct solution to the rational equation $$\frac{2}{x} = 4$$?

Accepted Answer

$$x = 0.5$$

Question 16

A circle has equation $$(x - 2)^2$ + (y + 3)^2$ = 16. $$What are the center and radius of the circle?

Accepted Answer

Center $$(2, -3)$$, radius $$4$$

Question 17

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

Accepted Answer

$$(x, y) = (3, 2)$$

Question 18

Which of the following is the correct application of the change of base formula for $$\log_5$(20)$$?

Accepted Answer

$$\log_5$(20) = \frac{\log_{10}(20)}{\log_{10}(5)}$$

College Algebra Syllabus and Success Guide – MATH 1314

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