Explanation

Solve: (2x + 3) / (x - 1) = 3

2x + 3 = 3(x - 1)  

2x + 3 = 3x - 3  

3 + 3 = 3x - 2x  

x = 6

Last verified on 04-05-2026

Explanation

Put x = -2 and y = 3 in x³y² + x²y  

x³ = (-2)³ = -8  

x² = (-2)² = 4  

y² = 3² = 9  

So x³y² = -8 x 9 = -72  

And x²y = 4 x 3 = 12  

Now add both: -72 + 12 = -60  

Last verified on 05-09-2026

Explanation

The equation |-x| = 0 simplifies to x = 0 since the absolute value of any number is zero only when the number itself is zero.

Therefore, the solution set contains only {0}.

Last verified on 05-09-2026

Explanation

Given:

P = Q + 8 = x + 8

R = 2 x Q = 2x  

S = P - 4 = (x + 8) - 4 = x + 4

Total = 92

So: Q + P + R + S = 92

x + (x + 8) + 2x + (x + 4) = 92

5x + 12 = 92

5x = 92 - 12

5x = 80

x = 16

Check:

Q = 16

P = 16 + 8 = 24

R = 2 x 16 = 32

S = 24 - 4 = 20

Total = 16 + 24 + 32 + 20 = 92

Answer: 16 pilgrims, giving P 24, R 32 and S 20

Last verified on 11-09-2026

Explanation

Let correct answers = x and wrong answers = 34 − x.

Score equation: 2.5x − 1(34 − x) = 67

Therefore: 3.5x − 34 = 67 → 3.5x = 101 → x = 28.857

Since the number of correct answers must be a whole number, the stated score of 67 is impossible.

Last verified on 10-09-2026

Explanation

32 = 2⁵

So, 2^(x+3) = 2⁵

Therefore, x + 3 = 5

x = 2

Last verified on 11-07-2026

Explanation

Divide 100 by 4: 

100 / 4 = 25 with remainder 0

When remainder = 0, i^n = i^4 = 1

Last verified on 25-08-2026

Explanation

Moduli of (3 + 4i)

Formula for modulus of a + bi = sqrt(a^2 + b^2)

Here a = 3 , b = 4

Modulus = sqrt(3^2 + 4^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

Last verified on 25-08-2026

Explanation

Addition of 5y + 4 and 3x + 3y + 1

= 5y + 4 + 3x + 3y + 1

= 3x + 5y + 3y + 4 + 1

= 3x + 8y + 5

Last verified on 25-08-2026

Explanation

Write 32 as a power of 2  

2 x 2 x 2 x 2 x 2 = 32  

So 32 = 2^5  

Compare with the given equation  

2^x = 32  

2^x = 2^5  

If the bases are the same, the powers must be equal  

x = 5

Last verified on 23-08-2026