Explanation

The trigonometric identity is:

Sec²θ - Tan²θ = 1

Explanation

Let's break it down step by step:

1. (√9²+12²) = √(81+144) = √225 = 15

2. (-3)² = 9

3. 15 + 9 = 24

4. (-1 + 2 + 3) = 4, and 4³ = 64

5. 24 - 64 = -40

6. ³√-125 = -5 (since (-5)³ = -125)

7. -40 - (-5) = -40 + 5 = -35

Explanation

Let's evaluate each statement:

1. -5 + 1 = -4 (not 4), so this statement is false.

2. 4 - 5 = -1 (true)

3. 2 + (-1) = 1 (true)

4. -7 + (-6) = -13 (true)

Explanation

15 divided by -3:

15 ÷ (-3) = -5

Explanation

Let's solve the equations:

1. x + y = 5

2. x - y = 3

Add both equations:

2x = 8

x = 4

Now, substitute x = 4 in equation (1):

4 + y = 5

y = 1

The solution is (4, 1).

Explanation

A surd is an irrational number or expression containing a square root, cube root, etc., that can't be simplified to a rational number.

Example: √2, ³√5 are surds because they involve radical signs.

Explanation

The power set P(A) of a set A with n elements has 2^n elements.

Here, A = {a, b, c, d, e} has 5 elements, so n = 5.

The number of elements in P(A) is 2^5 = 32.

Explanation

The expression ad - bc is called the Determinant of A, denoted as |A|.

Explanation

If |A| ≠ 0, then matrix A is Non-singular (also known as invertible).

Explanation

The notation n√x^m can be rewritten in power form as:

(x^m)^(1/n) = x^(m/n)