Q: The length of a vegetable garden is 7 feet longer than its width. If the area of the garden is 78 square feet, what are its dimensions?

$$6 \text{ ft by } 13 \text{ ft}$$

Question 1

Which of the following is the standard form of the complex number $$5 + 5i - (-4 + i)$$?

Accepted Answer

$$9 + 4i$$

Question 2

Simplify $$2(1 + 7i^2$)$$ and write the answer in the form $$a + bi.$$

Accepted Answer

$$-12$$

Question 3

Find the product of $$3i$$ and its conjugate $$-3i. $$Write the answer in the form $$a + bi.$$

Accepted Answer

$$-9$$

Question 4

Write the expression $$\dfrac{2i}{1 - i} in $$standard form $$a + bi.$$

Accepted Answer

$$1 + i$$

Question 5

Simplify $$\dfrac{5 - 2i}{2 + 3i}$$ and write the answer in the form $$a + bi.$$

Accepted Answer

$$\dfrac{4 - 19i}{13}$$

Question 6

Perform the operation $$\sqrt{3} - \sqrt{-121}$$ and write the result in standard form.

Accepted Answer

$$\sqrt{3} - 11i$$

Question 7

Solve the quadratic equation $$3x^2 + 2x = 8$ for x$.

Accepted Answer

$$x = 1, x = -\dfrac{8}{3}$$

Question 8

What number must be added to $$x^2 + 9x$ to make it a perfect square trinomial?

Accepted Answer

$$\left(\dfrac{9}{2}\$$right)^2$$ = 20.25$$

Question 9

Solve the equation $$x^2 - 4x - 13 = 0$ by completing the square.

Accepted Answer

$$x = 2 \pm \sqrt{17}$$

Question 10

A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 112 feet per second. The distance $$s (in $$feet) of the ball from the ground after $$t$$ seconds is $$s = 128 + 112t - 16t^2$. After how many seconds does the ball strike the ground?

Accepted Answer

$$8$$

Question 11

The length of a vegetable garden is 7 feet longer than its width. If the area of the garden is 78 square feet, what are its dimensions?

Accepted Answer

$$6 	ext{ ft by } 13 	ext{ ft}$$

Question 12

Solve the radical equation $$\sqrt{x + 32} = x.$$

Accepted Answer

$$x = 8$$

Question 13

Solve the rational inequality $$\dfrac{x - 1}{x + 6} \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -6) \cup (1, \infty)$$

Question 14

Which of the following is the solution to $$x^2 + 2x - 100 = 0$?

Accepted Answer

$$x = 8, x = -10$$

Question 15

Solve the equation $$x^3$$ + $$8x^2$$ \u003e x + 8$$.

Accepted Answer

$$(-\infty, -3) \cup (1, \infty)$$

Question 16

Find all real solutions to $$3x^3 + 10x$$ = $$7x^2.$$

Accepted Answer

$$x = 0, x = 2, x = -\dfrac{7}{3}$$

Question 17

Solve the equation $$6x^6$$ - $$25x^3 - 27 = 0$ by making an appropriate substitution.

Accepted Answer

$$x = 3, x = -1, x = -\dfrac{3}{2}$$

Question 18

Solve the equation $$2/3 - 4x$$^{1/3}$$ - 5 = 0$$ for $$x.$$

Accepted Answer

$$x = -27$$

Question 19

Solve the rational inequality $$\dfrac{x - 2}{x + 4} \leq 4$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -4) \cup [-2, \infty)$$

Question 20

Solve the rational inequality $$\dfrac{x}{x + 6} \u003c x$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -3) \cup (0, \infty)$$

College Algebra: Complex Numbers, Quadratics, and Equations Study Guide

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