2x > 10 => x > 5. The smallest integer satisfying this is 6.

-2x < -2 => x > 1. The solution is x > 1.

Using the quadratic formula x = [-b ± √(b^2 - 4ac)] / 2a, we find the roots are -2 ± i.

Substituting n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.

The argument of a complex number a + bi is given by tan^(-1)(b/a). Here, it is π since the point lies on the negative x-axis.

Using the binomial theorem, the coefficient of x^3 is given by C(5,3) * (2)^3 * (3)^(5-3) = 10 * 8 * 9 = 720.

The coefficient is C(8,4) = 70.

The coefficient is C(6,3) * (2)^3 = 20 * 8 = 160.

The constant term occurs when x^0, which is C(7,0) * (3)^0 * (-4)^7 = 1 * 1 * -16384 = -16384.

Using the power rule, f'(x) = 20x^3 - 12x^2 + 3.

Using the chain rule, f'(x) = 2e^(2x).

Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).

Using point-slope form: y - 3 = 5(x - 2) simplifies to y = 5x - 10.

Substituting x = 2 into the expression gives 3(2^2) - 2(2) + 1 = 12 - 4 + 1 = 9.

The modulus is calculated as √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

This is the Fibonacci sequence where each term is the sum of the two preceding ones. The next term is 3 + 5 = 8.

The differences between terms are 3, 5, 7, which increase by 2 each time. The next difference is 9, so 18 + 9 = 27.

There are 26 red cards in a deck of 52, so the probability is 26/52 = 1/2.

The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a. Here, c = 9 and a = 1, so the product is 9.

Rearranging the equation to slope-intercept form (y = mx + b), we get y = (2/3)x + 2. The slope (m) is 2/3.

-x < -2 => x > 2. The solution set is x > 2.

The sum of the coefficients is (1 + 1)^5 = 2^5 = 32.

This is a geometric series with a = 1 and r = 1/2. The sum of the first n terms is S_n = a(1 - r^n) / (1 - r). Here, S_5 = 1(1 - (1/2)^5) / (1 - 1/2) = 1(1 - 1/32) / (1/2) = 2(31/32) = 62/32 = 1.9375.

The differences are 3, 5, 7, 9, which increase by 2. The next difference is 11. The terms are 2, 5, 10, 17, 26, 37. The sum is 2 + 5 + 10 + 17 + 26 + 37 = 97.

The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. Here, -3/1 = -3.

cos(0°) = 1

i^4 = (i^2)^2 = (-1)^2 = 1.

sin(30°) = 0.5

Setting y = 0 gives 5x = 10, thus x = 2.

3x > 6 => x > 2. The value 3 satisfies the inequality.