Explanation

To simplify 5/(2 - √3), rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (2 + √3):

Step 1: Multiply by the conjugate

(5 / (2 - √3)) * ((2 + √3) / (2 + √3))

= (5(2 + √3)) / ((2 - √3)(2 + √3))

Step 2: Simplify the denominator

(2 - √3)(2 + √3) = 2² - (√3)²

= 4 - 3

= 1

Step 3: Simplify the expression

(5(2 + √3)) / 1

= 10 + 5√3

Explanation

Given the point (3, -4), where x = 3 (positive) and y = -4 (negative):

Step 1: Determine the quadrant

In the Cartesian coordinate system, Quadrant IV has positive x-coordinates and negative y-coordinates.

Explanation

The trigonometric identity is:

1 + cot²θ = csc²θ

Explanation

The nth term is given by n(n-1). To find the 11th term, substitute n = 11:

Step 1: Calculate the 11th term

11th term = 11(11 - 1)

= 11 * 10

= 110

Explanation

Explanation

Matrix B = [4 2; 6 5] (assuming it's a 2x2 matrix)

The determinant |B| = (4 × 5) - (2 × 6) = 20 - 12 = 8

Explanation

Step 1: Solve the inequality

x + 3 < 9

x < 9 - 3

x < 6

Explanation

Step 1: Isolate x

6x - 4 = 3x + 8

6x - 3x = 8 + 4

3x = 12

Step 2: Solve for x

x = 12 / 3

x = 4

Explanation

Step 1: Solve for x

3x + 5x = -8

8x = -8

x = -8 / 8

x = -1

Step 2: Calculate 2x + 1

2x + 1 = 2(-1) + 1

= -2 + 1

= -1

Explanation

Evaluate the polynomial at x = 4

3(4)³ - 2(4)² - 150

= 3(64) - 2(16) - 150

= 192 - 32 - 150

= 10