Explanation

Since y ∝ x, we have y = kx for some constant k.

When x = 4, y = 16:  

16 = k × 4 → k = 4  

Now for x = 6:  

y = 4 × 6 = 24  

Last verified 13-05-2026

Explanation

4x - 3x = 7 + 5  

x = 12

Last verified on 13-05-2026

Explanation

Roots of x² - 5x + 4 = 0:  

x² - 5x + 4 = (x - 1)(x - 4) → roots are 1 and 4  

Increase each by 1:  

New roots = 1 + 1 = 2, and 4 + 1 = 5  

New equation with roots 2 and 5:  

(x - 2)(x - 5) = x² - 7x + 10

Last verified on 13-05-2026

Explanation

Let the roots be r and r + 2, since they differ by 2.

For x² - px + 35 = 0:

Product of roots = r(r + 2) = 35  

Sum of roots = r + (r + 2) = 2r + 2 = p  

Solve r(r + 2) = 35:  

r² + 2r - 35 = 0  

(r + 7)(r - 5) = 0  

So r = 5 or r = -7  

Case 1: r = 5 → roots are 5 and 7 → p = 5 + 7 = 12  

Case 2: r = -7 → roots are -7 and -5 → p = -7 + (-5) = -12  

So p = 12 or -12

Last verified on 13-05-2026

Explanation

(a + bi)(a - bi) is a standard identity:  

(a + bi)(a - bi) = a² - (bi)² = a² - b²i² = a² - b²(-1) = a² + b²

So a² + b² = 37 directly.

Last verified on 13-05-2026

Explanation

a:b = 6:7 and b:c = 7:8  

Since b is 7 in both ratios, we can join them directly:  

a:b:c = 6:7:8  

So a:c = 6:8  

Simplify: 6:8 = 3:4

Last verified on 09-05-2026

Explanation

• Diameter = 2 × radius

• So, diameter is twice (2 times) the radius.

• It passes through the center of the circle.

Last verified on 09-05-2026

Explanation

Mean = sum of numbers ÷ count of numbers  

= (4 + 6 + 8 + 10) ÷ 4  

= 28 ÷ 4  

= 7

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

• Area of triangle = ½ × base × height.

• If base is halved and height is doubled, the effect cancels out.

• So, the area remains unchanged (same).

Last verified on 09-05-2026