Question 1

Which of the following correctly expresses $$\sqrt{-25} in $$terms of $$i$$?

Accepted Answer

$$5i$$

Question 2

Simplify $$(-2 - 4i) + (5 + 2i) - (3 - 6i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

Question 3

Multiply and simplify: $$(5 + 7i)(5 - 7i). $$What is the result?

Accepted Answer

$$74$$

Question 4

Solve the quadratic equation $$x^2 - 8x = 0$ using the zero product property.

Accepted Answer

$$x = 0 or$$ $$x = 8$$

Question 5

Given the quadratic equation $$x^2 + 2x - 3 = 0$, use the quadratic formula to find the solutions.

Accepted Answer

$$x = 1 or$$ $$x = -3$$

Question 6

For the equation $$x^2 + 4x + 4 = 0$, what is the value of the discriminant and how many real solutions does it have?

Accepted Answer

Discriminant $$= 0$$, one real solution

Question 7

Solve the equation $$2x^2 - 3x - 5 = 0$ using the quadratic formula.

Accepted Answer

Question 8

Alina takes a boat 6 miles downstream with a 1.5 mph current. The return trip against the current takes 1 hour longer. If $$b is $$the speed of the boat in still water, which equation models the scenario?

Accepted Answer

$$\frac{6}{b + 1.5} = \frac{6}{b - 1.5} + 1$$

Question 9

Solve the absolute value equation $$|2t - 3| = 6.$$

Accepted Answer

$$t = \frac{9}{2} or$$ $$t = -\frac{3}{2}$$

Question 10

Solve the inequality $$4x - 10 \leq 2x + 6$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, 8]$$

Question 11

Suppose a machine dispenses 8 fluid ounces of orange juice with a measurement error of no more than 0.05 ounces. Which absolute value inequality represents the possible values for $$x$$, the actual amount dispensed?

Accepted Answer

$$|x - 8| \leq 0.05$$

Question 12

Shanice has test scores of 96, 84, 80, 98, and 88. Her online homework score is 100 (weighted as one test grade). The final exam counts as two test grades. What score does she need on the final exam to have an average of at least 90?

Accepted Answer

At least $$94$$

Question 13

Solve the compound inequality $$5 \u003c 2x + 7 \leq 11$$ and write the solution set in interval notation.

Accepted Answer

$$( -1, 2 ]$$

Question 14

Which of the following is the correct solution to the absolute value inequality $$|x - 5| \u003e 0$$?

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 15

Solve for $$r in $$the formula $$V = \pi r^2$ h.$$

Accepted Answer

$$r = \sqrt{\frac{V}{\pi h}}$$

Question 16

Which of the following is the correct solution to the equation $$|x + 2| = -4$$?

Accepted Answer

No solution

Question 17

If $$a + bi is a $$complex number, which of the following statements is true?

Accepted Answer

The real part is $$a$$ and the imaginary part is $$b$$

Question 18

Solve the equation $$x^2 = 64$ using the square root property.

Accepted Answer

$$x = 8 or$$ $$x = -8$$

Question 19

Which of the following best describes the roots of the equation $$x^2 + 2x + 5 = 0$?

Accepted Answer

Two nonreal solutions

College Algebra Study Notes: Complex Numbers, Quadratic Equations, and Inequalities

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