What are all the subsets of the set?
{–1, 9}
(1 point)
Responses
empty set, {–1}, {9}
Image with alt text: empty set , {–1}, {9}
{–1}, {9}, {–1, 9}
{–1}, {9}, {–1, 9}
empty set, {–1}, {9}, {–1, 9}
Image with alt text: empty set , {–1}, {9}, {–1, 9}
{–1}, {0}
The correct answer is: empty set, {–1}, {9}, {–1, 9}
Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set, and P = {2, 4, 6, 8, 10}. What is upper P superscript single-quote baseline?
(1 point)
Responses
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
{3, 5, 7, 9}
{3, 5, 7, 9}
{1, 3, 5, 7, 9}
{1, 3, 5, 7, 9}
{2, 4, 8}
The correct answer is: {1, 3, 5, 7, 9}
Which compound inequality and graph represent the following phrase?
all real numbers that are greater than –4 and less than 4
(1 point)
Responses
–4 < x < 4
Choice A
–4 < x < 4 Image with alt text: Choice A
4 < x ≤ –4
Choice B
4 < x ≤ –4 Image with alt text: Choice B
–4 ≤ x ≤ 4
Choice C
–4 ≤ x ≤ 4 Image with alt text: Choice C
–4 ≤ x < 4
Choice D
The correct answer is: –4 < x < 4 (Choice A)
What are the solutions of the compound inequality? Graph the solutions.
–4 < 2x – 12 < 8
(1 point)
Responses
–4 < x < 8
Choice A
–4 < x < 8 Image with alt text: Choice A
4 < x < 10
Choice B
4 < x < 10 Image with alt text: Choice B
8 ≤ x ≤ 20
Choice C
8 ≤ x ≤ 20 Image with alt text: Choice C
4 < x ≤ 6
Choice D
Let's solve the compound inequality step by step:
-4 < 2x - 12 < 8
First, let's solve the left inequality:
-4 < 2x - 12
Add 12 to all parts of the inequality:
8 < 2x
Divide both sides by 2:
4 < x
Now, let's solve the right inequality:
2x - 12 < 8
Add 12 to all parts of the inequality:
2x < 20
Divide both sides by 2:
x < 10
So, the solutions to the compound inequality are 4 < x < 10.
The correct answer is: 4 < x < 10 (Choice B)
Graph:
Image with alt text: Graph showing an open circle at x = 4 and an open circle at x = 10, with a line segment between the two points representing the range 4 < x < 10.
What are the solutions of the equation? Graph and check the solutions.
|x| + 6 = 4
(1 point)
Responses
–8 to 8 number line
Image with alt text: –8 to 8 number line
x = –6 or x = 6
Choice B
x = –6 or x = 6 Image with alt text: Choice B
x = –4 or x = 4
Choice C
x = –4 or x = 4 Image with alt text: Choice C
x = –2 or x = 2
Choice D
To find the solutions of the equation |x| + 6 = 4, we need to isolate the absolute value expression.
|x| + 6 = 4
Subtract 6 from both sides of the equation:
|x| = -2
Since the absolute value of any real number is always non-negative, there are no solutions to this equation.
The correct answer is: There are no solutions (empty set).
What are the solutions of the equation? Graph and check the solutions.
X over 3 plus 1 equals 0
(1 point)
Responses
–10 to 10 number line
Image with alt text: –10 to 10 number line
x = –3
Choice B
x = –3 Image with alt text: Choice B
x = –3 or x = 3
Choice C
x = –3 or x = 3 Image with alt text: Choice C
x = –2
Choice D