Question 1

Solve the equation $$9x + 11 = 7x + 1. $$What is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 2

Simplify $$\sqrt{-90}$$ and write your answer in standard form.

Accepted Answer

$$3\sqrt{10}i$$

Question 3

Which of the following is the result of $$(5 - i)(3 + 4i)$$?

Accepted Answer

$$19 + 17i$$

Question 4

Solve the quadratic equation $$x^2 + 2x - 35 = 0$ by factoring.

Accepted Answer

$$x = 5 or$$ $$x = -7$$

Question 5

A square flower bed is enlarged by adding 2 meters to each side. If the area of the larger square is 196 square meters, what is the length of a side of the original square?

Accepted Answer

$$12$$ meters

Question 6

Jill can paint a fence in 18 hours, and her sister Jan can do it in 12 hours. How long will it take them to paint the fence together?

Accepted Answer

$$7\dfrac{1}{5}$$ hours

Question 7

Solve the inequality $$-5x - 4 \geq 3(2x - 5). $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, 1]$$

Question 8

The cost to produce $$x$$ units of earbuds is $$C = 3x + 1500$$ and the revenue is $$R = 8x. $$For what values of $$x$$ will the company at least break even?

Accepted Answer

$$[300, \infty)$$

Question 9

Solve the equation $$|4x + 7| = 0.$$

Accepted Answer

$$x = -\dfrac{7}{4}$$

Question 10

A projectile is launched upward from the ground. Its height in feet after $$t$$ seconds is $$s = -16t^2$ + 320t. $$After how many seconds will it hit the ground?

Accepted Answer

$$20$$ seconds

Question 11

Solve the equation $$x^2 + 10 = 0$ using the square root property.

Accepted Answer

$$x = \pm \sqrt{10}i$$

Question 12

Solve the quadratic equation $$8x^2 - 4x + 1 = 0$ by completing the square.

Accepted Answer

$$x = \dfrac{1}{4} \pm \dfrac{i}{4}$$

Question 13

Solve the equation $$\dfrac{3}{4}x + \dfrac{5}{5} = \dfrac{5}{5}x - \dfrac{2}{5}.$$

Accepted Answer

$$x = 6$$

Question 14

The length of a rectangle is 4 meters longer than its width. If the area is 8 square meters, what are the rectangle's dimensions (rounded to the nearest tenth)?

Accepted Answer

$$1.5$$ meters by $$5.5$$ meters

Question 15

Solve the inequality $$|2x + 9| \leq 3. $$Express your answer in interval notation.

Accepted Answer

$$[-6, -3]$$

Question 16

Which of the following is the simplified form of $$(4 - 3i)^2$?

Accepted Answer

$$7 - 24i$$

Question 17

Solve the quadratic equation $$2x^2 + 10x = 0$ by factoring.

Accepted Answer

$$x = 0 or$$ $$x = -5$$

Question 18

Solve the equation $$|5x - 1| = 2x + 3.$$

Accepted Answer

$$x = -2 or$$ $$x = \dfrac{4}{7}$$

Question 19

The longer leg of a right triangle exceeds the shorter leg by 1 inch, and the hypotenuse exceeds the longer leg by 7 inches. What are the lengths of the legs (rounded to the nearest tenth)?

Accepted Answer

$$17.6$$ inches and $$18.6$$ inches

Question 20

Solve the inequality $$x^2 + 3x - 4$$ \leq 0$$ and express your answer in interval notation.

Accepted Answer

$$[-4, 1]$$

College Algebra Exam Review: Step-by-Step Guidance

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