Using the sum of roots, b = - (4 + (-1)) = -3.

For the roots to be equal, the discriminant must be zero, which means b^2 = 4ac.

For the roots to be equal, the discriminant must be zero. Thus, 2^2 - 4*1*k = 0 leads to k = 1.

For the roots to be equal, the discriminant must be zero. Thus, 4^2 - 4(1)(k) = 0 leads to k = 4.

The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.

Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

For the roots to be equal, the discriminant must be zero. Thus, (-5)² - 4(1)(k) = 0, giving k = 25/4 = 6.25.

If A · B = 0, then A and B are orthogonal (perpendicular) to each other.

A · B = |A||B|cos(θ) => 15 = 5*3*cos(θ) => cos(θ) = 1, θ = 0°.

If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.

If A · B = |A||B|, then cos(θ) = 1, which means θ = 0°.

A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, hence it is a right-angled triangle.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Variance is the square of the standard deviation. Therefore, variance = 7² = 49.

Variance is the square of the standard deviation. Therefore, variance = 3² = 9.

The sum of the first n natural numbers is given by the formula n(n + 1)/2 = 210. Solving n(n + 1) = 420, we find n = 14 or n = 15. Thus, n = 15.

The nth term of the series can be found using T_n = S_n - S_(n-1). First, calculate S_10 and S_9: S_10 = 3(10^2) + 2(10) = 320, S_9 = 3(9^2) + 2(9) = 273. Thus, T_10 = S_10 - S_9 = 320 - 273 = 47.

From Vieta's formulas, p = -sum of roots = -5 and q = product of roots = 6.

The sum of the roots is -p = 8, hence p = -8.

The sum of the roots is given by -(-3)/1 = 3. Thus, k = 3 - 3 = 0.

The sum of the roots is given by -(-6)/1 = 6. The product of the roots is k, and since the sum is correct, k can be any value.

Angles that sum up to 90 degrees are called complementary angles.

Two angles whose sum is 90 degrees are called complementary angles.

The numbers are 4 and 8, as 4 + 8 = 12 and 4 × 8 = 32.

Standard deviation = √16 = 4. If the minimum is 0, the maximum can be 4, thus range = 4 - 0 = 4.

Standard deviation is the square root of variance. Therefore, SD = √16 = 4.

Standard deviation = √25 = 5.

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.