Explanation

x - 3 =4

x = 4 + 3

x = 7

Explanation

The expression a(b + c −d) simplifies to:

ab + ac −ad

So, the correct option is: ac + ab - ad

Explanation

Given matrix A = [1 0, 0 1]:

This is a Unit matrix or Identity matrix, where all elements on the main diagonal are 1, and the rest are 0.

Explanation

A scalar matrix is a diagonal matrix where all diagonal elements are equal (here, 2), and non-diagonal elements are zero.

Explanation

Calculating the Derivative

Given: f(x) = (3x^5 + 6)^5

Using the chain rule: f'(x) = 5(3x^5 + 6)^4 . d/dx(3x^5 + 6)

= 5(3x^5 + 6)^4 . 15x^4

= 75x^4(3x^5 + 6)^4

= (3x^5 + 6)^4 . 75x^4

Explanation

Explanation

Verifying the Options

Given: sqrt{49x^4 + 42x^3 + 79x^2 + 30x + 25}

Checking the Options

We've already verified that (7x^2 + 3x + 5)^2 = 49x^4 + 42x^3 + 79x^2 + 30x + 25

Explanation

Using the Given Equations

Given: a^2 + b^2 = 18 and a + b = 8

Squaring the Second Equation

(a + b)^2 = 8^2

a^2 + 2ab + b^2 = 64

Substituting a^2 + b^2 = 18

18 + 2ab = 64

Solving for ab

2ab = 64 - 18

2ab = 46

ab = 23

Explanation

Finding the Conjugate of z bar

Given: z = 3 + 4i

The conjugate of z, denoted as z bar, is 3 - 4i.

The conjugate of z bar is 3 + 4i.

Explanation