Explanation

a/b = 10/11 and b/c = 6/7  

Multiply them to get a/c:

a/c = (a/b) × (b/c) = (10/11) × (6/7) = 60/77

So a:c = 60:77

Last verified on 24-05-2026

Explanation

Mean = (Sum of numbers) / (Number of values)  

Mean = (12 + 14 + 16 + 18) / 4  

Mean = 60 / 4 = 15

Last verified on 24-05-2026

Explanation

• A diameter is the longest chord of a circle.
• Angle subtended by a diameter at the circumference is always 180°.
• This forms a straight line at the circle’s edge.
• It is based on circle geometry principles.

Last verified on 24-05-2026

Explanation

secθ = 1/cosθ, so  

secθ × cosθ = (1/cosθ) × cosθ = 1

Last verified on 24-05-2026

Explanation

We use sin²θ + cos²θ = 1  

cos²θ = 1 - sin²θ  

cos²θ = 1 - (7/25)²  

cos²θ = 1 - 49/625  

cos²θ = 576/625  

cosθ = ±√(576/625) = ±24/25

Sign depends on the quadrant of θ

Last verified on 24-05-2026

Explanation

If base = b, height = h, then area = b × h. 

New base = b × 1.20 = 1.2b  

New height = h × 0.80 = 0.8h  

New area = 1.2b × 0.8h = 0.96bh = 0.96 × original area

Last verified on 24-05-2026

Explanation

Put a = 9 in a² + b² = 145

9² + b² = 145

81 + b² = 145

b² = 145 - 81

b² = 64

b = ±8

Last verified on 24-05-2026

Explanation

• A triangle with all angles equal is an equilateral triangle.
• Each angle in this triangle is 60°.
• All sides are also equal in length.
• It is a regular and perfectly symmetrical triangle.

Last verified on 24-05-2026

Explanation

(10x + 6)/(x(x + 3)) decomposes as 2/x + 8/(x + 3)

Solution:

Let (10x + 6)/(x(x + 3)) = A/x + B/(x + 3)

Multiply both sides by x(x + 3)

10x + 6 = A(x + 3) + B(x)

Put x = 0

10(0) + 6 = A(0 + 3) + B(0)

6 = 3A

A = 2

Put x = -3

10(-3) + 6 = A(-3 + 3) + B(-3)

-30 + 6 = 0 - 3B

-24 = -3B

B = 8

So the decomposition is:

2/x + 8/(x + 3)

Last verified on 24-05-2026

Explanation

If f(x) = x² + 2x then f(2) + f(-2) = 8

Solution:

Put x = 2 in f(x) = x² + 2x

f(2) = 2² + 2_2

f(2) = 4 + 4 = 8

Put x = -2 in f(x) = x² + 2x

f(-2) = (-2)² + 2_(-2)

f(-2) = 4 - 4 = 0

Now add both values

f(2) + f(-2) = 8 + 0 = 8

Last verified on 24-05-2026