log_2(1/8) = log_2(2^-3) = -3.

log_5(1) = 0 because 5^0 = 1.

In the equation y^2 = 4px, we have 4p = 20, thus p = 5.

Using the identity, sin(180° - θ) = sin θ.

According to the Pythagorean identity, sin² θ + cos² θ = 1 for any angle θ.

The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.

The coefficient of x^4 in (x + 5)^6 is given by 6C4 * 5^2 = 15 * 25 = 375.

The discriminant D = b^2 - 4ac = 12^2 - 4*3*9 = 0, indicating equal roots.

The discriminant is b^2 - 4ac = 6^2 - 4(3)(2) = 36 - 24 = 12.

A matrix is singular if its determinant is zero. Det(A) = (x*4) - (2*3) = 4x - 6 = 0. Solving gives x = 1.5.

Rearranging gives 3x - 2x = 5 + 7, thus x = 12.

Solving for x gives 4x = 16, thus x = 4.

Add 5 to both sides: 4x = 16. Then divide by 4: x = 4.

Adding 7 to both sides gives 4x = 16. Dividing by 4 gives x = 4.

√(144) = 12 and √(64) = 8, so 12 + 8 = 20.

√(16) = 4 and √(25) = 5, so 4 + 5 = 9.

All values are the same, so variance = 0.

Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. Variance = [(1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²] / 6 = 2.92 (approx 2.5).

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 4.

All values are the same, so variance = 0.

All values are the same, so variance = 0.

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Substitute x = 1 into the equation to find y = -1.

The vertex can be found using x = -b/(2a). Here, x = 8/(2*2) = 2. Substituting x = 2 into f(x) gives f(2) = -3, so the vertex is (2, -3).

To find the x-intercept, set y = 0. Thus, 4x = 20, giving x = 5.

Rearranging to slope-intercept form: -2y = -5x + 10, thus y = (5/2)x - 5. The y-intercept is -5.

An identity matrix is defined as a square matrix with all diagonal elements equal to 1 and all other elements equal to 0.

A matrix where all elements are zero is called a zero matrix.

A scalar matrix is a square matrix in which all the elements are equal to the same scalar value.

A skew-symmetric matrix is defined by the property A = -A.

The difference of squares is given by a² - b² = (a + b)(a - b).