Explanation

Right triangle rule: a² + b² = c²  

c = 10, a = 6  

6² + b² = 10²  

36 + b² = 100  

b² = 100 - 36 = 64  

b = 8

Last verified on 09-05-2026

Explanation

Using Pythagoras: a² + b² = c² for right triangle  

8² + 15² = 64 + 225 = 289  

17² = 289  

Since 8² + 15² = 17², it follows the right triangle rule.

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

Explanation

x² - 3x + 2 = 0  

This splits as (x - 1)(x - 2) = 0  

So the roots are x = 1 and x = 2

If we multiply each root by 2:  

1 × 2 = 2  

2 × 2 = 4  

New roots are 2 and 4

To make the equation with roots 2 and 4:  

(x - 2)(x - 4) = 0  

x² - 4x - 2x + 8 = 0  

x² - 6x + 8 = 0

Last verified on 09-05-2026

Explanation

Factors are (x - m)(x - n) = x² - (m + n)x + mn  

So m + n = p and mn = 30  

Numbers that multiply to 30 and differ by 1: 5 and 6, or -5 and -6  

So p = 5 + 6 = 11 or p = -5 + (-6) = -11

Last verified on 09-05-2026

Explanation

(a + bi)(a - bi) = a² - (bi)² = a² - b²i²

Since i² = -1, this becomes a² - b²(-1) = a² + b²

Given (a + bi)(a - bi) = 29, so a² + b² = 29

Last verified on 09-05-2026

Explanation

• Area of triangle = ½ × base × height.
• If base is doubled and height remains same, area also doubles.
• So, new area becomes 2 times the original area.

Last verified on 08-05-2026