Question 1

Given the functions $f(x) = 8 + 4(3x)$ and $g(x) = 3(x - 6) + 10$, for which value of $x$ do $f(x)$ and $g(x)$ have the same value?

Accepted Answer

$x = 30$

Question 2

What is the zero of the function $f(x) = 2[2x - (3x - 7)] - 6(x - 7)$?

Accepted Answer

$x = 7$

Question 3

Solve the equation $8x - 5x = 9x - 36$.

Accepted Answer

$x = 9$

Question 4

For the rational equation $\frac{2}{x-3} = \frac{9}{x+3} + \frac{7}{x-3}$, which values of $x$ make the denominators zero?

Accepted Answer

$x = 3$ and $x = -3$

Question 5

Electrostuff manufactures Electrogadget IV. The average cost per unit is modeled by $f(x) = \frac{24,000 + 280x}{x}$. How many units must be produced for the average cost per unit to be $440$?

Accepted Answer

$150$ units

Question 6

When $80\%$ of a number is added to the number, the result is $144$. What is the number?

Accepted Answer

$80$

Question 7

You inherit $10,000$ and must invest it in two stocks paying $6\%$ and $11\%$ annual interest. If the total interest earned for the year is $900$, how much should be invested at $6\%$?

Accepted Answer

$4,000$

Question 8

After a $9\%$ price reduction, a boat sold for $28,210$. What was the boat's price before the reduction?

Accepted Answer

$31,000$

Question 9

A rectangular room's length is $7$ feet longer than twice its width. If the perimeter is $194$ feet, what is the width?

Accepted Answer

$30$ ft.

Question 10

Perform the operation and write the expression in standard form $a + bi$: $(3 - 7i) - (2 + 4i)$.

Accepted Answer

$5 - 11i$

Question 11

Solve the quadratic equation $x^2 = 20x + x$.

Accepted Answer

$x = -4$ and $x = 5$

Question 12

A ladder $10$ feet long is $6$ feet from the base of a wall. How far up the wall does the ladder reach?

Accepted Answer

$8$ ft.

Question 13

An open box is made from a square sheet of cardboard by cutting out $4$-inch squares from each corner and folding. If the box is to have a volume of $400$ cubic inches, what are the original dimensions of the sheet?

Accepted Answer

$18$ in. by $18$ in.

Question 14

You have $600$ feet of fencing to enclose a rectangular plot that borders a river. If you do not fence the side along the river, what is the largest area that can be enclosed?

Accepted Answer

$45,000$ ft^2$

Question 15

Solve the linear inequality $24 - 20x + 4(5x - 6) \leq -x - 4$. Write your answer in interval notation.

Accepted Answer

$(-\infty, 1]$

Question 16

Use interval notation to represent all values of $x$ satisfying $f(x) = 4x - 5$, $g(x) = 3x - 9$, and $f(x) > g(x)$.

Accepted Answer

$(-4, \infty)$

Question 17

Solve the compound inequality $5 \leq 14 - 9x < 29$. Write your answer in interval notation.

Accepted Answer

$[3, 12)$

Question 18

Greg estimates his cost function as $C(x) = 9000 + 0.09x$ and his revenue function as $R(x) = 1.95x$, where $x$ is the number of cars washed in six months. Find the number of cars that must be washed for Greg to make a profit. Write your answer in interval notation.

Accepted Answer

$[4839, \infty)$

Unit 2 Exam Review – Applications and Problem Solving in College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards