Explanation

Given:

a:b = 8:9

b:c = 3:4

Make b equal in both ratios (LCM of 9 and 3 is 9):

a:b = 8:9

b:c = 9:12

Now combine:

a:b:c = 8:9:12

So, a:c = 8:12 = 2:3

Last verified on 15-05-2026

Explanation

Mean = (6 + 8 + 10 + 12) ÷ 4

= 36 ÷ 4

= 9

Last verified on 15-05-2026

Explanation

A tangent is a line that touches a circle at exactly one point.

It does not cut the circle, it only touches it.

Last verified on 15-05-2026

Explanation

Using trigonometric identity:

tanθ = sinθ/cosθ

So, sinθ divided by cosθ is equal to tanθ.

Last verified on 15-05-2026

Explanation

Given: sinθ = 8/17

cosθ = √(1 − (8/17)²)

= √(1 − 64/289)

= √(225/289)

= 15/17

Last verified on 15-05-2026

Explanation

Area of triangle = ½ × base × height

If base becomes 2b and height becomes 2h:

New area = ½ × (2b) × (2h)

= 4 × (½ × b × h)

So, area becomes 4 times the original.

Last verified on 15-05-2026

Explanation

Given:

a² + b² = 65

a = 1

Put value of a:

1² + b² = 65

1 + b² = 65

Subtract 1 from both sides:

b² = 64

Take square root:

b = 8 (positive value)

So, b = 8.

Last verified on 15-05-2026

Explanation

• A scalene triangle has all three sides of different lengths.
• It also has all angles unequal.

Last verified on 15-05-2026

Explanation

The decomposition is:

(8x + 6)/[x(x + 2)] = A/x + B/(x + 2)

Multiply both sides by x(x + 2) so the denominators cancel out:

8x + 6 = A(x + 2) + Bx

Now find A and B:

Put x = 0. That makes the Bx term zero, so 6 = 2A. That gives A = 3.  

Put x = -2. That makes the A(x + 2) term zero, so -10 = -2B. That gives B = 5.

So it equals 3/x + 5/(x + 2).

Last verified on 15-05-2026

Explanation

Given y = 18 when x = 3:

18 = k(3²)

18 = 9k

k = 2

Now for x = 5:

y = 2(5²)

y = 2 × 25

y = 50

Last verified on 15-05-2026