Question 1

What is the quotient of $$\frac{5}{-9i}$$ written in standard form $$a + bi$$?

Accepted Answer

$$\frac{5}{-9i} = \frac{5}{-9i} \cdot \frac{i}{i} = \frac{5i}{-9i^2$} = \frac{5i}{9} = \frac{5}{9}i$$

Question 2

Solve $$\frac{5i}{2 + i}$$ and write your answer in standard form $$a + bi.$$

Accepted Answer

$$1 + 2i$$

Question 3

Solve the quadratic equation $$8x^2 - 71x = 9$ by factoring. What are the solutions?

Accepted Answer

$$x = -\frac{1}{8}, x = 9$$

Question 4

Solve $$4x^2 - 3x + 1 = 0$ by completing the square. What are the solutions?

Accepted Answer

$$x = \frac{3 \pm i}{8}$$

Question 5

Given $$(2x - 1)(x + 1) = 6$$, solve for $$x$$ using the quadratic formula.

Accepted Answer

$$x = -1 \pm \frac{\sqrt{57}}{4}$$

Question 6

Find the discriminant of $$x^2 - 4x + 3 = 0$ and determine the number and type of roots.

Accepted Answer

Discriminant $$D = 4$$, two real unequal roots

Question 7

A rectangular storage room has a length 2 feet longer than its width. If the area is 120 square feet, what are its dimensions?

Accepted Answer

10 ft by 12 ft

Question 8

A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in $$t$$ seconds is $$s(t) = -16t^2$ + 171t. At $$what time(s) will the rocket be 118 ft from the ground? Round to the nearest tenth.

Accepted Answer

0.7 and 9.9 sec

Question 9

Solve the equation $$\frac{2}{2x} - \frac{3}{x + 1} = 1 by $$multiplying both sides by the least common denominator (LCD). What are the solutions?

Accepted Answer

$$x = -3 \pm \frac{\sqrt{13}}{2}$$

Question 10

Solve the equation $$x - 2 = \frac{3}{x}$$ for $$x.$$

Accepted Answer

$$x = -1, x = 3$$

Question 11

Solve the equation $$x - \frac{3x - 2}{4} = 9$$ for $$x.$$

Accepted Answer

$$x = 9$$

Question 12

Solve the equation $$3x + 10 = x$$ for $$x.$$

Accepted Answer

$$x = 5$$

Question 13

Solve the equation $$2x + 3 - \frac{x + 1}{2} = 1$$ for $$x.$$

Accepted Answer

$$x = -1, x = 3$$

Question 14

Solve $$(x + 5)^2$ + 9(x + 5) + 18 = 0 by $$making an appropriate substitution.

Accepted Answer

$$x = -11, x = -8$$

Question 15

Solve $$x^4$$ - $$29x^2 + 100 = 0$ by substitution. What are the solutions?

Accepted Answer

$$x = -2, x = 2, x = -5, x = 5$$

Question 16

Ron takes two hours more than Paul to mow the lawn. Working together, they can mow the lawn in 5 hours. How long does it take each of them working alone?

Accepted Answer

Paul: 9.1 hr; Ron: 11.1 hr

Question 17

Solve the inequality $$6x - 1 \leq 5x - 6$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, -5]$$

Question 18

Solve the combined inequality $$-23 \leq -3x - 2 \u003c -14$$ and write the solution in interval notation.

Accepted Answer

$$(4, 7]$$

Question 19

Solve the rational inequality $$\frac{x}{x - 4} \u003c 3$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 4) \cup (6, \infty)$$

College Algebra Test #1 Review – Step-by-Step Study Guidance

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