The numbers in the set {x|x= a/b, where a, b are integers and b ≠ 0} are called numbers. List the numbers in the set below that are (a) Natural numbers, (b) Integers, (c) Rational Numbers, (d) Irrational numbers, (e) Real numbers

B = {-7, 1/4 , - 1.6666..., π, 4, 7}

Given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8} and
C = {1, 3, 4, 6)

Find the sets:
A U B
A ∩ C
(A U B) ∩ C
(A ∩ B)’
A’
A’ U B’

Use set notation to describe the Venn diagrams below

The universal set U is defined as follows:

U = {x:x∈N,2
The sets M and R are subsets of U such that

M = {odd numbers}
R = {square numbers}

List the numbers of the subset M.
List the number of the subset R.
Draw a Venn diagram that represents the relationship among the defined subset of U.

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

sweetheart, there isn't a cube below.