Explanation

Given the equation 20 = 3x + 8:

Step 1: Subtract 8 from both sides.

20 - 8 = 3x

12 = 3x

Step 2: Divide both sides by 3.

x = 12 / 3

x = 4

Explanation

Given y = 3:

Step 1: Calculate y³.

y³ = 3³ = 27

Step 2: Calculate y³ - y.

y³ - y = 27 - 3 = 24

Step 3: Calculate y³(y³ - y).

y³(y³ - y) = 27 × 24

= 648

Explanation

Given x = -1 and y = -3:

Let's evaluate the expression 5y² - 2(x² - 4xy) - 5y:

1. Calculate 5y² = 5(-3)² = 5(9) = 45

2. Calculate x² = (-1)² = 1

3. Calculate 4xy = 4(-1)(-3) = 12

4. Calculate x² - 4xy = 1 - 12 = -11

5. Calculate -2(x² - 4xy) = -2(-11) = 22

6. Calculate -5y = -5(-3) = 15

Now, combine the results:

5y² - 2(x² - 4xy) - 5y = 45 + 22 + 15

= 82

Explanation

Given f(x) = x³ - (1/x³):

f(1/x) = (1/x)³ - (1/(1/x)³) = (1/x³) - x³

Now, let's calculate f(x) + f(1/x):

f(x) + f(1/x) = (x³ - 1/x³) + (1/x³ - x³)

= x³ - x³ - 1/x³ + 1/x³

= 0

Explanation

The set {x: x ∈ N, x ≤ 10} has 10 elements (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

The cardinality of the power set of a set with n elements is 2^n.

So, the cardinality of the power set is 2^10 = 1024.