Question 1

Given the points $$A(2, 3)$$ and $$B(8, 11)$$, what is the distance between them?

Accepted Answer

$$10$$

Question 2

Which of the following is the equation of the line passing through the points $$(1, 2)$$ and $$(4, 8)$$?

Accepted Answer

Question 3

A chemist is mixing two solutions. The first solution contains 30% salt and the second contains 80% salt. How many liters of each should be mixed to obtain 10 liters of a 50% salt solution?

Accepted Answer

4 liters of 30% and 6 liters of 80%

Question 4

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

Accepted Answer

$$f(g(2)) = 2 \cdot 4 + 3 = 11$$

Question 5

Which of the following is the inverse of the function $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{3}$$

Question 6

Solve the quadratic equation $$x^2 - 6x + 5 = 0$.

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 7

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$When does the ball hit the ground?

Accepted Answer

$$t = 0$$ and $$t = 2$$

Question 8

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

Accepted Answer

$$x 
eq 4$$

Question 9

Solve the inequality $$2x - 5 \u003e 7.$$

Accepted Answer

$$x \u003e 6$$

Question 10

Given $$f(x) = x^2$ - 4x + 7$$, what is the range of $$f(x)$$?

Accepted Answer

$$[3, \infty)$$

Question 11

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 12

Expand $$\log(2x^3$)$$ using logarithm properties.

Accepted Answer

$$\log 2 + 3\log x$$

Question 13

Solve the exponential equation $$2^{x+1} = 16$.

Accepted Answer

$$x = 3$$

Question 14

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$. How much of the substance remains after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.79$$

Question 15

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

Question 16

A business invests $$\5000$ in an account that earns 6% annual interest compounded monthly. What will the balance be after 5 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A \approx \6740.24$

Question 17

Which of the following is the solution to the system of equations: $$\begin{cases} x + y + z = 6 \ 2x - y + z = 3 \ x + 2y - z = 4 \end{cases}$$?

Accepted Answer

$$(x, y, z) = (1, 2, 3)$$

Question 18

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 19

Which of the following is the correct formula for the sum of a geometric series with first term $$a$$ and common ratio $$r ($$where $$|r| \u003c 1$$)?

Accepted Answer

$$S = \frac{a}{1 - r}$$

Math 142 Final Exam Review: College Algebra Study Guide

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