Question 1

Which of the following points is located in Quadrant II of the Cartesian coordinate system?

Accepted Answer

$$(-3, 5)$$

Question 2

What is the $$y-$$intercept of the graph of $$y = 4 - x^2$?

Accepted Answer

$$(0, 4)$$

Question 3

Given the equation $$y = |x + 1|$$, what is the $$x-$$intercept?

Accepted Answer

$$(-1, 0)$$

Question 4

A rational equation is an equation where at least one term is a fraction. What is the first step in solving a rational equation?

Accepted Answer

Note any restrictions that make the denominator zero.

Question 5

Solve for $$x$$: $$\frac{x-3}{4} = 5 - \frac{x+5}{7}$$

Accepted Answer

$$x = 12$$

Question 6

Which of the following equations is an identity?

Accepted Answer

$$x + 2 = x + 2$$

Question 7

A rectangular swimming pool is 6 meters less than twice the width. If the perimeter is 126 meters, what is the width?

Accepted Answer

$$w = 21$$

Question 8

What is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 9

Simplify: $$(5 + 4i) / (4 - i)$$ and write the result in standard form.

Accepted Answer

$$\frac{24}{17} + \frac{21}{17}i$$

Question 10

Which of the following is the quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 11

Use the discriminant to determine the number and type of solutions for $$x^2 - 4x + 4 = 0$.

Accepted Answer

One real solution

Question 12

Solve the radical equation: $$\sqrt{x + 3} + 3 = x$$

Accepted Answer

$$x = 6$$

Question 13

Express the interval $$(-1, 4] in $$set-builder notation.

Accepted Answer

$$\{x \mid -1 \u003c x \leq 4\}$$

Question 14

Solve the absolute value equation: $$3|3x - 1| + 6 = 24$$

Accepted Answer

$$x = \frac{3}{2} or$$ $$x = -\frac{7}{6}$$

Question 15

If $$|u|  0$$, what is the equivalent compound inequality?

Accepted Answer

$$-c \u003c u \u003c c$$

Question 16

Given the model $$d = 2.3n + 1.5$$ for the percentage of marriages ending in divorce when the wife is over 25, what is the predicted percentage after 10 years?

Accepted Answer

$$d = 24.5$$

Question 17

Solve the inequality $$2x + 5 \geq 4x - 5.$$

Accepted Answer

$$x \geq 5$$

Question 18

Which of the following is the complex conjugate of $$5 - 4i$$?

Accepted Answer

$$5 + 4i$$

Question 19

If you multiply both sides of an inequality by a negative number, what must you do to the inequality sign?

Accepted Answer

Reverse the inequality sign

College Algebra Chapter 1: Graphs, Equations, and Inequalities

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