Explanation

(3x + 2)/4 = (x + 6)/2

Multiply both sides by 4:

3x + 2 = 2(x + 6)

Expand RHS:

3x + 2 = 2x + 12

Collect x terms:

3x - 2x = 12 - 2

x = 10

Last verified on 25-05-2026

Explanation

Original: x² - 10x + 21 = 0  

Substitute x → x + 1:

(x + 1)² - 10(x + 1) + 21 = 0  

x² + 2x + 1 - 10x - 10 + 21 = 0  

x² - 8x + 12 = 0

Last verified on 25-05-2026

Explanation

Let the factors be (x - m) and (x - n)

Then:

m + n = p

m * n = 90

|m - n| = 9

Using (m - n)^2 = (m + n)^2 - 4mn:

9^2 = p^2 - 4*90

81 = p^2 - 360

p^2 = 441

p = ±21

Last verified on 25-05-2026

Explanation

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

So (a + bi)(a - bi) = a² + b² = 73

Last verified on 25-05-2026

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