Question 1

Solve the inequality $$|x-9| + 7 \u003c 9. $$Which of the following represents the solution set?

Accepted Answer

$$8 \u003c x \u003c 10$$

Question 2

Find the real solution to the equation $$\sqrt{7x-6} = 8.$$

Accepted Answer

$$x = 10$$

Question 3

Write the expression $$\frac{3}{8-8i} in $$standard form $$a+bi.$$

Accepted Answer

$$\frac{3}{32} + \frac{3}{32}i$$

Question 4

A circle has the equation $$x^2$$ + $$y^2 = 25$. What is the center and radius of the circle?

Accepted Answer

Center $$(0,0)$$, radius $$5$$

Question 5

Find the real solutions of $$3x^2 - 10x + 7 = 0$ using the quadratic formula.

Accepted Answer

$$x = 1, x = \frac{7}{3}$$

Question 6

A bank loaned out $$16,000$$, part at $$9\%$$ per year and the rest at $$17\%$$ per year. If the interest received in one year totaled $$2000$$, how much was loaned at $$9\%$$?

Accepted Answer

$$6,000$$

Question 7

Solve the equation $$4x - (7x + 9) = 4x - 16.$$

Accepted Answer

$$x = -7$$

Question 8

Find the equation of a line perpendicular to $$y = \frac{1}{9}x + 7$$ and containing the point $$(-5, 0). $$Express your answer in slope-intercept form.

Accepted Answer

$$y = -9x - 45$$

Question 9

Find the distance between the points $$P_1 = (-5$$, 4)$$ and P_2$ = (3, 2).$$

Accepted Answer

$$\sqrt{68}$$

Question 10

Solve $$(x-5)^2 = 64$ using the square root method.

Accepted Answer

$$x = 13 or$$ $$x = -3$$

Question 11

Given the function $$f(x) = \frac{4x}{\sqrt{x+8}}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq -8$$

Question 12

Use the discriminant to determine the nature of the solutions for $$4x^2 - 9x + 7 = 0$.

Accepted Answer

Two unequal real solutions

Question 13

Simplify $$-\sqrt{63} + 4\sqrt{175}.$$

Accepted Answer

$$13\sqrt{7}$$

Question 14

Refer to the graph in $$image_1. Is $$the graph a function? What is its domain?

Accepted Answer

Yes; $$[-3, 3]$$

Question 15

Refer to the graph in $$image_2. $$What are the coordinates of the vertex?

Accepted Answer

$$(5, -4)$$

Question 16

Refer to the graph in $$image_3. $$For what value(s) of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = -12, 0, 4, 8, 12$$

Question 17

Given the line $$y = x - 5$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$5$$, $$y-$$intercept: $$-5$$

Question 18

Solve the inequality $$15(x-12) \u003c x + 16$$ and express your answer in interval notation.

Accepted Answer

$$x \u003c 13.14$$

Question 19

Given points $$P = (-3, -4)$$ and $$Q = (-1, -1)$$, what is the equation of the line containing these points in slope-intercept form?

Accepted Answer

$$y = \frac{3}{2}x + \frac{1}{2}$$

Question 20

Refer to the graph in $$image_3. $$For what value(s) of $$x$$ does $$f(x) = -2$$?

Accepted Answer

$$x = -14, 4$$

College Algebra Final Exam Review – Step-by-Step Guidance

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