Explanation

Ladder + wall + ground make a right triangle.  

Angle = 45° at ground, distance from wall = 5m = adjacent side  

tan45° = opposite / adjacent = height / 5  

tan45° = 1, so height = 5 × 1 = 5m

Last verified on 24-06-2026

Explanation

3x² - 4√x + xy + √25x + 7x²  

1. Combine x²: 3x² + 7x² = 10x²  

2. √25x = √(25) × √x = 5√x  

3. Combine √x: -4√x + 5√x = +√x  

4. xy stays as is  

Result: 10x² + xy + √x

Last verified on 24-06-2026

Explanation

Let width = w

Height = w + 6

Perimeter of rectangle = 2(length + width)

= 2(w + (w + 6))

= 2(2w + 6)

= 4w + 12

Last verified on 24-06-2026

Explanation

x = 5, y = 2  

x + y = 5 + 2 = 7

Last verified on 24-06-2026

Explanation

When 39 is divided by 4:

• 4 × 9 = 36, remainder = 39 − 36 = 3
• When 39 is divided by 9:
• 9 × 4 = 36, remainder = 39 − 36 = 3

So in both cases remainder is 3, which satisfies the condition.

Last verified on 24-06-2026

Explanation

(-1)^300 

Rule: if power is even → 1, if power is odd → -1

300 is even

So (-1)^300 = 1

Last verified on 24-06-2026

Explanation

Look at the pattern: each term × 3  

2 → 6 → 18 → ? → ? → 486  

So 18 × 3 = 54

54 × 3 = 162  

162 × 3 = 486  

Full sequence: 2, 6, 18, 54, 162, 486  

Now "4th term from the last"  

Last = 486, 2nd last = 162, 3rd last = 54, 4th last = 18.

Last verified on 24-06-2026

Explanation

When a power is raised to another power, we multiply exponents:

(m¹⁄₃)³⁄₅ = m^(1/3 × 3/5) = m¹⁄₅

(n⁻²)³⁄₅ = n^(-2 × 3/5) = n⁻⁶⁄₅

So the simplified form is m¹⁄₅ n⁻⁶⁄₅.

Last verified on 24-06-2026

Explanation

Let width = w cm  

Then length = w + 6 cm  

Perimeter of rectangle = 2(length + width)  

2(w + 6 + w) = 48  

2(2w + 6) = 48  

4w + 12 = 48  

4w = 36  

w = 9 cm  

So width = 9 cm, length = 9 + 6 = 15 cm.

Last verified on 23-06-2026

Explanation

For quadratic ax² + bx + c = 0:  

Sum of roots = -b/a  

Product of roots = c/a  

Take a = 1, then:  

-b = sum = -2 → b = 2  

c = product = 3  

So equation: x² + 2x + 3 = 0

Last verified on 23-06-2026