What are all the subsets of the set?

Question

{–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}

Answer 1

The correct answer is: empty set, {–1}, {9}, {–1, 9}

Answer 2

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}

Answer 3

The correct answer is: {1, 3, 5, 7, 9}

Answer 4

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

Answer 5

The correct answer is: –4 < x < 4 (Choice A)

Answer 6

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

Answer 7

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.

Answer 8

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

Answer 9

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).

Answer 10

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

Answer 11

To find the solution of the equation (x/3) + 1 = 0, we can solve it as follows:

(x/3) + 1 = 0

Subtract 1 from both sides:

(x/3) = -1

Multiply both sides by 3 to isolate x:

x = -3

So, the solution to the equation is x = -3.

The correct answer is: x = -3 (Choice B)

Graph:
There is a horizontal line on the number line at x = -3.
Image with alt text: number line with a horizontal line at x = -3.