Question 1

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

Accepted Answer

$$x = 3$$

Question 2

Express the solution set of $$-3 \u003c 4x + 1 \u003c 9 in $$interval notation.

Accepted Answer

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

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