The slopes can be found by solving the quadratic equation derived from the given equation.

Using the quadratic formula, the slopes are found to be -3/5 and -2/5.

The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.

Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.

The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.

The sum of the roots is given by -b/a = 12/3 = 4.

The sum of the roots is given by -b/a = 7/1 = 7.

Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.

The sum of the roots is given by -b/a = 7/1 = 7.

(1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2.

Using the right triangle definition, cos(tan^(-1)(x)) = adjacent/hypotenuse = 1/√(1+x^2).

Using the right triangle definition, sin(tan^(-1)(x)) = opposite/hypotenuse = x/√(1+x^2).

sin^(-1)(-1) corresponds to the angle whose sine is -1, which is -π/2.

Since π/4 is in the range of sin^(-1), sin^(-1)(sin(π/4)) = π/4.

sin^(-1)(√3/2) corresponds to the angle whose sine is √3/2, which is π/3.

tan^(-1)(√3) corresponds to the angle whose tangent is √3, which is π/3.

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at (±3, 0).

The only solution is x = 0.

The solutions are x = 2π/3 and 4π/3.

The solutions are x = 2π/3 and x = 4π/3.

The solutions are x = π/4, 3π/4, 5π/4, and 7π/4.

The solutions are x = 0, π, and 2π.

sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.

The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.

Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.

The 75th percentile (Q3) is the value below which 75% of the data falls, which is 40.

a_7 = 2^7 + 3^7 = 128 + 2187 = 2315.