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 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 3

Which of the following is the correct simplified form of the expression $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$ for $$x 
eq 3$$?

Accepted Answer

Question 4

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 40x$$, 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 $$400 at$$ $$x = 10$$

Question 5

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + 2y = 7 \ 3x - y = 5 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 6

Which of the following is the correct domain of the function $$f(x) = \dfrac{1}{x^2$ - 4}$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = -2$$

Question 7

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

Accepted Answer

$$2 \cdot 9 + 1 = 19$$

Question 8

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

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 9

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.03t}$$, where A_0$ is the initial amount and t$ is in years. What is the half-life of the substance (rounded to the nearest year)?

Accepted Answer

$$24$$ years

Question 10

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

Accepted Answer

$$40$$

Question 11

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 12

A $$2 	imes 2$$ matrix $$A$$ has entries $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}. $$What is the determinant of $$A$$?

Accepted Answer

$$-2$$

Question 13

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

Accepted Answer

$$x = 32$$

Question 14

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

Accepted Answer

$$40.8$$ meters

Question 15

Which of the following is the correct simplified form of $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$7\sqrt{2}$$

Question 16

If $$a_n = 5 \cdot 2$$^{n-1}$$, what is the 4th term of the sequence?

Accepted Answer

$$40$$

Question 17

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

Accepted Answer

Question 18

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

Accepted Answer

$$x = 3$$

Question 19

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

Accepted Answer

$$(2, 3)$$

Question 20

A car’s value depreciates exponentially according to $$V(t) = 20000 \cdot 0.85^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years (rounded to the nearest dollar)?

Accepted Answer

$$15313$$

College Algebra (Math 124E/24) Syllabus and Course Guide

Guida di studio - Domande di pratica

Study guide - Flashcard