Q: Find the $x$- and $y$-intercepts for the equation $2x + 3y = 6$.

$x$-intercept: $(3, 0)$; $y$-intercept: $(0, 2)$

Q: Suppose a person invests a total of $10,000$ in two accounts. One account earns $5\%$ annually, and the other earns $6\%$ annually. If the total interest earned from both accounts in a year is $560$, how much is invested in each account?

$6,000$ at $5\%$, $4,000$ at $6\%$

Question 1

Solve for $x$ in the equation $5x - 7 = 2x + 8$.

Accepted Answer

$x = 3$

Question 2

Express the solution set of $-3 < 4x + 1 < 9$ in interval notation.

Question 3

Solve for $x$ in the equation $2(x - 5) = 3(x + 2) - 4$.

Accepted Answer

$x = 8$

Question 4

Given the relation $\{(3,3), (1,-1), (0,-3), (a, b)\}$, which of the following could be a value for $(a, b)$ so that the relation is a function?

Accepted Answer

$(2, 4)$

Question 5

Find the $x$- and $y$-intercepts for the equation $2x + 3y = 6$.

Accepted Answer

$x$-intercept: $(3, 0)$; $y$-intercept: $(0, 2)$

Question 6

Given $y = x + 2$, identify the slope and $y$-intercept.

Accepted Answer

Slope: $1$, $y$-intercept: $2$

Question 7

Find the equation of the line parallel to $3x - y = 5$ that passes through the point $(-1, 4)$.

Accepted Answer

$y = 3x + 7$

Question 8

Suppose a person invests a total of $10,000$ in two accounts. One account earns $5\%$ annually, and the other earns $6\%$ annually. If the total interest earned from both accounts in a year is $560$, how much is invested in each account?

Accepted Answer

$6,000$ at $5\%$, $4,000$ at $6\%$

Question 9

In May, Jack bought a used Ford Mustang with a $5.0\%$ interest rate. The total price, which includes the price of the used car plus sales tax, was $17,481$. If the sales tax rate was $7.25\%$, what was the price of the car?

Accepted Answer

$16,300$

Question 10

The length of a rectangle is $3$ meters less than twice the width. The perimeter is $18$ meters. Find the width.

Accepted Answer

$4$ meters

Question 11

A store sells apples for $1.00$ and oranges for $2.00$. A customer pays $14$ for $10$ items. Find the number of each item.

Accepted Answer

$6$ apples, $4$ oranges

Question 12

Solve and graph: $2x + 5 = 9$.

Accepted Answer

$x = 2$

Question 13

Given $f(x) = x^2 - x$ and $g(x) = x + 4$, find $(f \circ g)(1)$.

Accepted Answer

$15$

Question 14

Solve the system: $2x - 3y = 1$ and $x + 4y = 5$.

Accepted Answer

$x = 3$, $y = 0.5$

Question 15

Which of the following best describes the domain of the function $f(x) = \sqrt{x - 2}$?

Accepted Answer

$x \geq 2$

Question 16

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

Accepted Answer

$9$

Question 17

A chemical solution contains $x$ grams of substance A and $y$ grams of substance B. If the total mass is $50$ grams and substance A is twice as heavy as substance B, what are the values of $x$ and $y$?

Accepted Answer

$x = 33.3$, $y = 16.7$

Question 18

Which of the following is the range of the function $f(x) = x^2 - 4$?

Accepted Answer

$y \geq -4$

Question 19

A line passes through the points $(2, 3)$ and $(4, 7)$. What is its equation in slope-intercept form?

Accepted Answer

$y = 2x - 1$

Question 20

If $f(x) = \frac{1}{x}$, which of the following is the domain of $f$?

Accepted Answer

$x 
eq 0$

Study Notes: Key Concepts in College Algebra and Trigonometry

Study Guide - Practice Questions

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