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

144 = 2 × 2 × 2 × 2 × 3 × 3, which simplifies to 2⁴ × 3².

This is the correct prime factorization, using only prime numbers.

Explanation

If AB = O (null matrix), it is possible that either A = O (null matrix) or B = O (null matrix), or both could be null matrices.

In matrix multiplication, if either matrix is a null matrix, the result will always be a null matrix.

Explanation

Given:

1. 6x + 2y = 6300

2. 2x + y = 2600

Multiplying equation (2) by 2:

4x + 2y = 5200

Subtracting:

(6x + 2y) - (4x + 2y) = 6300 - 5200

2x = 1100

x = 550

Explanation

Given x - 1/2x} = 6,

Cubing both sides gives x^3 - 1/8x^3 - 3.1/2.6 = 216.

This simplifies to x^3 - 1/8x^3 - 9 = 216.

So, x^3 - 1/8x^3 = 216 + 9 = 225.

Explanation

Given:

5x + 8 = 23

Subtract 8 from both sides:

5x = 23 - 8

5x = 15

Divide both sides by 5:

x = 15 / 5

x = 3

Explanation

(-9) - (-9)

= -9 + 9 (since subtracting a negative is equivalent to adding a positive)

= 0

Explanation

To solve for x, add 7 to both sides of the equation:

2x - 7 + 7 = -8 + 7

2x = -1

Divide both sides by 2:

x = -1/2

Explanation

To simplify the expression, follow the order of operations:

2(7x - 3) + 5(-2x + 6)

Distribute the coefficients:

14x - 6 - 10x + 30

Combine like terms:

4x + 24

Explanation

Given A = {x | x ∈ P ∧ 5 ≤ x ≤ 13}, where P is the set of prime numbers:

The prime numbers between 5 and 13 are 5, 7, 11, and 13.

So, A = {5, 7, 11, 13}, which has 4 elements.

The power set P(A) has 2^n elements, where n is the number of elements in A:

2^4 = 16