Question 1

Which of the following is the correct solution set for the inequality $$2x - 5 \leq 9$$?

Accepted Answer

$$x \leq 7$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the quadratic function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18$$ thousand dollars at $$x = 2$$ thousand units.

Question 3

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 4

A ball is thrown upward from the top of a 50-meter building with an initial velocity of $$20 m/s. $$Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 50. $$After how many seconds does the ball hit the ground?

Accepted Answer

Question 5

Which of the following is the correct factorization of the polynomial $$x^3$$ - $$4x^2 - 7x + 10$?

Accepted Answer

$$(x - 5)(x + 1)(x - 2)$$

Question 6

If $$f(x) = 3x^2$ - 2x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 7

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

Accepted Answer

$$x = 32$$

Question 8

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 time in years. If the initial amount is 100$ grams, how much remains after 10$ years? (Round to the nearest gram.)

Accepted Answer

$$74$$ grams

Question 9

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x^2$ - 9}$$?

Accepted Answer

$$x 
eq 3$$ and $$x 
eq -3$$

Question 10

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

Accepted Answer

$$x = 11$$

Question 11

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. If your total bill was $$\50$, how many miles did you drive?

Accepted Answer

$$100$$ miles

Question 12

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

Accepted Answer

$$x = 3$$

Question 13

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

Accepted Answer

$$f(g(2)) = 0$$

Question 14

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

Accepted Answer

$$x = 4 or$$ $$x = \dfrac{2}{3}$$

Question 15

A rectangular garden has a length that is 3 meters more than twice its width. If the area is $$99$$ square meters, what are the dimensions of the garden?

Accepted Answer

Width $$= 6 m$$, Length $$= 15 m$$

Question 16

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

Accepted Answer

$$55$$

Question 17

If $$x^2 + 6x + 8 = 0$, what are the solutions for x$?

Accepted Answer

$$x = -2$$ and $$x = -4$$

Question 18

Which of the following is the inverse function of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 5}{2}$$

Question 19

A bank offers an annual interest rate of $$6\%$$ compounded quarterly. If you invest $$\1000$, how much will you have after 2$ years? (Round to the nearest dollar.)

Accepted Answer

$$1127$$

Question 20

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

Accepted Answer

$$x = 1$$

College Algebra Syllabus and Course Overview

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드