Question 1

Which of the following is the correct equation for the line passing through the points $(5, 3)$ and $(-1, 8)$?

Accepted Answer

$y = -rac{5}{6}x + rac{43}{6}$

Question 2

A car dealer reduces the list price of its vehicles by $14\%$. If one vehicle has a sale price of $\$28,809.99$, what was its original list price to the nearest cent?

Accepted Answer

$\$33,489.53$

Question 3

Solve the equation $x^3 - 2x^2 + \frac{3}{2}x + 4 = 0$ to two decimal places. Which of the following is a solution?

Accepted Answer

$x \approx -2.13$

Question 4

A rock falls from a height of $20$ meters. Its height after $t$ seconds is given by $y = 20 - 4.9t^2$. When does the rock hit the ground? (Round to two decimal places)

Accepted Answer

$t \approx 2.02$ seconds

Question 5

Find the domain of $f(x) = \frac{3}{x^2 + 4x - 12}$.

Accepted Answer

$x 
eq -6, x 
eq 2$

Question 6

A motorboat travels on a river that has a current of $3$ mph. The trip upstream takes $5$ hours and the return trip downstream takes $2.5$ hours. What is the speed of the boat in still water?

Accepted Answer

$8$ mph

Question 7

How much water should be added to $300$ milliliters of a $60\%$ acid solution to make a $50\%$ acid solution?

Accepted Answer

$60$ mL

Question 8

An electric company charges a flat monthly fee of $\$12.76$ plus $0.18$ per kilowatt-hour. Which equation gives the monthly charge $C$ for $x$ kilowatt-hours?

Accepted Answer

$C = 12.76 + 0.18x$

Question 9

The volume $V$ of a gas in a closed container varies inversely with its pressure $P$. If $V = 600$ cm$^3$ when $P = 150$ mm Hg, what is $V$ when $P = 200$ mm Hg?

Accepted Answer

$V = 450$ cm$^3$

Question 10

Find and simplify $(f \circ g)(x)$ for $f(x) = 8x - 5$ and $g(x) = x^2 - 2x$.

Accepted Answer

$8x^2 - 16x - 5$

Question 11

Solve the system of equations: $\begin{cases} 2x - y = 5 \ 3x - 3y = 9 \end{cases}$

Accepted Answer

$x = 3, y = 1$

Question 12

If the area of a rectangle is $108$ square inches and the perimeter is $42$ inches, what are the dimensions of the rectangle?

Accepted Answer

$9$ in by $12$ in

Question 13

An $8\%$ solution and a $15\%$ solution are to be mixed to obtain $20$ ounces of a $10\%$ solution. How much of the $8\%$ solution should be used? (Round to two decimal places)

Accepted Answer

$14.29$ oz

Question 14

Two cyclists leave a city at the same time, one going east and the other west. The westbound cyclist bikes $5$ mph faster than the eastbound cyclist. After $6$ hours, they are $246$ miles apart. How fast is the eastbound cyclist riding?

Accepted Answer

$21$ mph

Question 15

Find the domain of $h(x) = \sqrt{2 + 5x}$.

Accepted Answer

$x \geq -0.4$

Question 16

The resistance $R$ of a wire varies directly with its length $L$ and inversely with the square of its diameter $d$. If a wire $1.2$ meters long and $0.5$ centimeters in diameter has a resistance of $140$ ohms, what is the resistance of a wire made from the same material that is $3$ meters long and has a diameter of $0.8$ centimeters? (Round to two decimal places)

Accepted Answer

$131.25$ ohms

Question 17

Which of the following is the equation of a line parallel to $3x + 4y = 2$ and passing through $(4, 1)$?

Accepted Answer

$3x + 4y = 16$

Question 18

Solve for $x$: $\sqrt{x - 3} = 0$

Accepted Answer

$x = 3$

Question 19

Find the equation of a line with undefined slope passing through $(5, 7)$.

Accepted Answer

$x = 5$

Question 20

Find the domain of $g(x) = \frac{9 + x}{16x - 4x^2}$.

Accepted Answer

$x 
eq 0, x 
eq 4$

College Algebra Study Guide: Equations, Functions, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards