The coefficient of x^4 in (2x - 5)^6 is given by 6C2 * (2)^4 * (-5)^2 = 15 * 16 * 25 = 600. The coefficient is -720.

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

The coefficient of x^5 is given by C(8, 5) = 56.

The discriminant is b^2 - 4ac = 12^2 - 4(3)(12) = 144 - 144 = 0.

The discriminant is b^2 - 4ac = 12^2 - 4*3*9 = 144 - 108 = 36.

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.

The term containing x^4 is given by C(6, 4)(3x)^4(4)^2 = 15 * 81 * 16 = 19440.

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

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

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

The modulus |z| = √((-1)² + (-1)²) = √(1 + 1) = √2.

|−8| = 8 and |−3| = 3, so 8 + 3 = 11.

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

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

The vertex can be found using x = -b/(2a). Here, x = 12/(2*3) = 2. Substituting x = 2 into the equation gives y = 3(2)^2 - 12(2) + 7 = -5.

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).

A complex number z lies on the unit circle if |z| = 1. For z = 1 + 0i, |z| = √(1² + 0²) = 1. For z = 0 + 1i, |z| = √(0² + 1²) = 1. Both 1 + 0i and 0 + 1i lie on the unit circle.

√4 = 2, 0.25 = 1/4, and 1 is rational. √2 is irrational.

0.125 is equal to 1/8.

0.25 is equal to 1/4.

log_10(0.01) = log_10(10^-2) = -2.

log_2(32) = log_2(2^5) = 5.

√3 is an irrational number, while 1/2, 0, and 3 are rational.

The conjugate of a complex number z = a + bi is given by z* = a - bi. Here, the conjugate is 2 + 3i.

The conjugate of z = 5 - 2i is z* = 5 + 2i.

The conjugate of a complex number z = a + bi is given by z* = a - bi. Here, the conjugate of 5 - 3i is 5 + 3i.

The smallest positive integer is 1.

log_10(0.1) = log_10(10^-1) = -1.

log_a(b) + log_a(c) = log_a(bc) by the product property of logarithms.