Explanation

x² − 7x + 12 = 0

Factorize: (x − 3)(x − 4) = 0

So, x = 3 or x = 4

Last verified on 10-05-2026

Explanation

3x − 7 = 11

3x = 11 + 7

3x = 18

x = 18 ÷ 3 = 6

Last verified on 09-05-2026

Explanation

(x + 1)(x + 2)(x + 3) = 210

Put x = 4 → (5)(6)(7) = 210

So the correct value of x is 4.

Last verified on 10-05-2026

Explanation

3x + 24 = 16

3x = 16 − 24
3x = −8
x = −8 ÷ 3
x = −8/3

Last updated question NS on 09 MAY 2026

Explanation

For any angle θ:  

sin²θ + cos²θ = 1

Last verified on 09-05-2026

Explanation

sinθ = opposite/hypotenuse = 12/13  

Use Pythagoras: opposite² + adjacent² = hypotenuse²  

12² + adjacent² = 13²  

144 + adjacent² = 169  

adjacent² = 25  

adjacent = 5

cosθ = adjacent/hypotenuse = 5/13

Last verified on 09-05-2026

Explanation

Let (6x + 4)/x(x + 2) = A/x + B/(x + 2)  

Multiply both sides by x(x + 2):  

6x + 4 = A(x + 2) + Bx  

Find A: put x = 0  

6(0) + 4 = A(0 + 2) + B(0) → 4 = 2A → A = 2  

Find B: put x = -2  

6(-2) + 4 = A(-2 + 2) + B(-2) → -12 + 4 = -2B → -8 = -2B → B = 4  

So (6x + 4)/x(x + 2) = 2/x + 4/(x + 2)

Last verified on 09-05-2026

Explanation

f(3) = 2 × 3² = 2 × 9 = 18  

f(1) = 2 × 1² = 2 × 1 = 2  

f(3) - f(1) = 18 - 2 = 16

Last verified on 09-05-2026

Explanation

y ∝ x² means y = k × x²

Find k:  

y = 8 when x = 2  

8 = k × 2²  

8 = k × 4  

k = 2

So y = 2x²

When x = 3:  

y = 2 × 3² = 2 × 9 = 18

Last verified on 09-05-2026

Explanation

Cross multiply:  

3(x - 5) = 2(x - 1)  

3x - 15 = 2x - 2  

3x - 2x = -2 + 15  

x = 13

Last verified on 09-05-2026