Explanation

To find the inverse of 3 in modulo 7, we need to find a number x such that:

3x ≡ 1 (mod 7)

We can try multiplying 3 by each number from 1 to 6:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9 ≡ 2 (mod 7)

3 × 4 = 12 ≡ 5 (mod 7)

3 × 5 = 15 ≡ 1 (mod 7)

So, the inverse of 3 in modulo 7 is 5.

Explanation

0.009/x = 0.01

To isolate x, we can divide both sides by 0.009, which gives us:

1/x = 0.01/0.009

1/x = 1.111 (approximately)

Now, take the reciprocal of both sides:

x = 1/1.111

x ≈ 0.9

So, the value of x is approximately 0.9.

Explanation

Given:

(x1 + x2 + x3 + x4) / 4 = 16

Multiply both sides by 4:

x1 + x2 + x3 + x4 = 64 ... (Equation 1)

Also, (x2 + x3 + x4) / 2 = 23

Multiply both sides by 2:

x2 + x3 + x4 = 46 ... (Equation 2)

Now, substitute Equation 2 into Equation 1: x1 + 46 = 64

Subtract 46 from both sides: x1 = 18

Therefore, the correct answer is: 18

Explanation

Given:

a^2 + b^2 = 8 ... (Equation 1)

(a - b)^2 = 4

Expanding the left side of the equation: a^2 - 2ab + b^2 = 4

Now, substitute Equation 1 into this equation: 8 - 2ab = 4

Subtract 8 from both sides: -2ab = -4

Divide both sides by -2: ab = 2

So, the value of ab is 2.

Explanation

Explanation

Explanation

Explanation

For matrices A × B ≠ B × A in general, so matrix multiplication is not commutative.

However, matrix addition is commutative and associative, and matrix multiplication is associative, but not commutative.

Explanation

• Distribute the 2 across the terms inside the parentheses:
  

$2(x^2+y^2+xy)=2x^2+2y^2+2xy$

Explanation

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs. (39 x 3) = Rs. 117.

Therefore Principal = Rs. (815 - 117) = Rs. 698.