Explanation

y ∝ x means y = kx  

Find k: 10 = k(2) → k = 5  

So y = 5x  

When x = 7: y = 5(7) = 35  

Last verified on 08-05-2026

Explanation

2(x + 1) = x + 7  

2x + 2 = x + 7  

2x - x = 7 - 2  

x = 5  

Last verified on 08-05-2026

Explanation

x² - 6x + 8 = 0 → (x - 2)(x - 4) = 0  

Roots: 2 and 4  

Increase each by 1: new roots are 3 and 5  

New equation: (x - 3)(x - 5) = x² - 8x + 15 = 0  

Last verified on 08-05-2026

Explanation

Let the roots be r and r + 2.  

Product of roots = 24  

r(r + 2) = 24  

r² + 2r - 24 = 0  

(r + 6)(r - 4) = 0  

r = 4 or r = -6  

Sum of roots = p  

If r = 4: roots are 4 and 6 → p = 4 + 6 = 10  

If r = -6: roots are -6 and -4 → p = -6 + (-4) = -10  

Last verified on 08-05-2026

Explanation

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

Given (a + bi)(a - bi) = 17  

So a² + b² = 17  

Last verified on 08-05-2026

Explanation

a : b = 5 : 6  

b : c = 2 : 3 = 6 : 9  

So a : b : c = 5 : 6 : 9  

Therefore a : c = 5 : 9  

Last verified on 08-05-2026

Explanation

Mode = value that appears most often  

4 appears 3 times, more than any other number  

Last verified on 08-05-2026

Explanation

• A tangent is a straight line that touches a circle at only one point.
• This point is called the point of contact.
• Unlike a secant, it does not cut the circle at two points.

Last verified on 08-05-2026

Explanation

cotθ = 1/tanθ  

So tanθ × cotθ = tanθ × (1/tanθ) = 1  

Last verified on 08-05-2026

Explanation

cosθ = adjacent/hypotenuse = 12/13  

Use sin²θ + cos²θ = 1  

sin²θ = 1 - (12/13)² = 1 - 144/169 = 25/169  

sinθ = ±5/13  

If we assume θ is in quadrant I, then sinθ = 5/13  

Last verified on 08-05-2026