Explanation

a:b = 7:8

b:c = 4:5

Make b same:

a:b = 14:16

b:c = 16:20

Therefore, a:c = 14:20 = 7:10.

Last verified on 14-05-2026

Explanation

Mean = (5 + 7 + 9) ÷ 3

= 21 ÷ 3

= 7

Last verified on 14-05-2026

Explanation

• A chord that passes through the center of a circle is called a diameter.
• It is the longest chord of the circle.

Last verified on 14-05-2026

Explanation

Using trigonometric identity:

tan²θ + 1 = sec²θ

So, tan²θ + 1 = sec²θ.

Last verified on 14-05-2026

Explanation

Given cosθ = 5/13

sinθ = √(1 − 25/169)

= √(144/169)

= 12/13

Last verified on 14-05-2026

Explanation

Area of triangle = ½ × base × height

If height is multiplied by 3, area also becomes 3 times.

Last verified on 13-05-2026

Explanation

Let other side = x

25² = 7² + x²

625 = 49 + x²

x² = 576

x = 24

Last verified on 13-05-2026

Explanation

Check using Pythagoras theorem:

9² + 40² = 81 + 1600 = 1681

41² = 1681

Since LHS = RHS, it is a right triangle.

Last verified on 13-05-2026

Explanation

(7x + 5)/[x(x + 1)] = A/x + B/(x + 1)

7x + 5 = A(x + 1) + B(x)

Put x = 0: 5 = A(1) => A = 5

Put x = -1: -2 = B(-1) => B = 2

(7x + 5)/[x(x + 1)] = 5/x + 2/(x + 1)

Last verified on 13-05-2026

Explanation

f(2) = 2² + 1 = 4 + 1 = 5  

f(3) = 3² + 1 = 9 + 1 = 10  

f(2) + f(3) = 5 + 10 = 15  

Last verified on 13-05-2026