Explanation

In direct variation, two variables increase or decrease together, and are related by a = kb, where k is a constant.

If k = 1, then a = b, which expresses direct variation.

Explanation

In the Cartesian coordinate system:

• 1st quadrant: (+, +)
• 2nd quadrant: (-, +)
• 3rd quadrant: (-, -)
• 4th quadrant: (+, -)

Given point P(-4, -7):

Both x (-4) and y (-7) coordinates are negative.

This point lies in the 3rd quadrant.

Explanation

The shaded part in the Venn diagram represents Q - P, meaning elements that belong to set Q but not to P.

Explanation

To simplify the expression, follow the rules of exponents:

(x⁴)³ = x^(4×3) = x¹²

Now, divide x¹² by x⁻⁴:

x¹² ÷ x⁻⁴ = x¹² × x⁴ (since dividing by x⁻⁴ is the same as multiplying by x⁴)

= x^(12+4)

= x¹⁶

Explanation

Given that x = 3 is a solution to the equation:

x² + rx - 20 = 4

Substitute x = 3 into the equation:

(3)² + r(3) - 20 = 4

Simplify:

9 + 3r - 20 = 4

Combine like terms:

3r - 11 = 4

Add 11 to both sides:

3r = 15

Divide by 3:

r = 5

Explanation

The value that should be added to the polynomial to make it perfectly divisible by x + 1 is 0.

Explanation

Let's check each pair in the equation:

2x + 3y = 24

{6, 4} → 2(6) + 3(4) = 12 + 12 = 24 ✓

{12, 0} → 2(12) + 3(0) = 24 + 0 = 24 ✓

{0, 8} → 2(0) + 3(8) = 0 + 24 = 24 ✓

{9, -2} → 2(9) + 3(-2) = 18 - 6 = 12 ✗

Explanation

The correct answer is (a) trichotomy property of real numbers.

The trichotomy property states that for any two real numbers a and b, exactly one of the following must be true: a > b, a = b, or a < b. 

Explanation

Given:

x̄ (mean) = 12

∑x (sum) = 132

The formula for mean is:

x̄ = ∑x / n

Rearrange to find n:

n = ∑x / x̄

= 132 / 12

= 11

Explanation

Solve:

=√16+9 

=√(25)

=5

SH5-9-2023