Q: Which of the following is the correct reduced row echelon form (REF) for the augmented matrix $$\begin{bmatrix} 1 & 2 & | & 5 \\ 3 & -1 & | & 4 \end{bmatrix}$$?

$$\begin{bmatrix} 1 & 0 & | & 2 \\ 0 & 1 & | & 1.5 \end{bmatrix}$$

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 population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 2$$^{t/3}$$

Question 3

Which of the following is the correct solution to $$|3x - 5| = 7$$?

Accepted Answer

$$x = 4, x = -\frac{2}{3}$$

Question 4

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

Accepted Answer

$$x = 2, y = 1.5$$

Question 5

Which of the following is the correct line of best fit for the data points $$(1,2), (2,4), (3,6)$$?

Accepted Answer

$$y = 2x$$

Question 6

Solve the equation $$\log_2$(x - 1) = 3.$$

Accepted Answer

Question 7

Which of the following is the correct reduced row echelon form (REF) for the augmented matrix $$\begin{bmatrix} 1 & 2 & | & 5 \ 3 & -1 & | & 4 \end{bmatrix}$$?

Accepted Answer

$$\begin{bmatrix} 1 & 0 & | & 2 \ 0 & 1 & | & 1.5 \end{bmatrix}$$

Question 8

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 9

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$. How much remains after 10 years?

Accepted Answer

$$A(10) = 100e$$^{-0.5}$$ \approx 60.65$$

Question 10

Solve for $$x$$: $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 11

Which of the following is a complex zero of $$x^2 + 4 = 0$?

Accepted Answer

$$x = 2i$$

Question 12

Which equation represents a rational function?

Accepted Answer

$$f(x) = \frac{2x + 1}{x - 3}$$

Question 13

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 3(4) - 7 = 5$$

Question 14

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

Accepted Answer

$$x = 4$$

Question 15

A chemist mixes two solutions: one with 30% acid and one with 50% acid. If she wants 10 liters of a 40% acid solution, how many liters of each should she use?

Accepted Answer

5 liters of each solution

Question 16

Which of the following is the correct solution to $$\frac{2x}{x-1} = 4$$?

Accepted Answer

Question 17

Which of the following best describes the end behavior of $$f(x) = -2x^3$ + 5x^2$ - x + 7 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 18

If $$\log_{10}(x) = 2$$, what is $$x$$?

Accepted Answer

$$x = 100$$

Question 19

Which of the following is the correct solution to $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 20

A business’s profit $$P is $$modeled by $$P = 5000e$$^{0.03t}$$, where t$ is years since opening. What is the profit after 5 years?

Accepted Answer

$$P = 5000e$$^{0.15}$$ \approx 5811.31$$

College Algebra I: Final Exam Review (Chapters 1–6, 12) – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard