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?

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

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

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

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 $\dfrac{x - 1}{x + 6} > 0$ 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 $x^3 + 8x^2 > x + 8$.

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 $\dfrac{x}{x + 6} < x$ and express the solution in interval notation.

Accepted Answer

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

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

Study Guide - Practice Questions

Study Guide - Flashcards