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)

Explanation

Using the change of base formula:

log_b^a / log_b^d = log_d^a

Explanation

Let's expand both expressions:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

Now, add them:

(a + b)² + (a - b)² = a² + 2ab + b² + a² - 2ab + b²

= 2a² + 2b²

Explanation

Let's use the Pythagorean theorem:

Height of pole (perpendicular) = 12m

Length of string (hypotenuse) = 20m

Distance between foot of pole and end point of string (base) = √(hypotenuse² - perpendicular²)

= √(20² - 12²)

= √(400 - 144)

= √256

= 16m