Explanation

Explanation

0.5x + 5 = x - 0.75

Solving for x:

1. Move 0.5x to the right side:
   5 = x - 0.75 - 0.5x
2. Simplify:
   5 + 0.75 = x - 0.5x
   5.75 = 0.5x
3. Divide by 0.5:
   x = 11.5

Explanation

Area = 1/2 × (sum of bases) × altitude

48 = 1/2 × (14 + 18) × altitude

48 = 1/2 × 32 × altitude

48 = 16 × altitude

Altitude = 48/16 = 3 cm.

Explanation

Factorize the quadratic expression.

3x^2 - 9x + 6 = 3(x^2 - 3x + 2)

= 3(x^2 - 2x - x + 2)

= 3(x(x - 2) - 1(x - 2))

= 3(x - 1)(x - 2)

Explanation

The given quadratic expression is x² - 2x + 1.

This can be factored as:

x² - 2x + 1 = (x - 1)(x - 1)

= (x - 1)²

The answer is (x - 1)(x - 1).

Explanation

Add minutes: 52 min + 12 min = 64 min → 1 hour 4 min

Add hours: 6 h + 9 h = 15 h, plus 1 hour from minutes = 16 h

So, total = 16 h 04 min

Explanation

Given:

Cost Price (CP) = Rs. 1500

Selling Price (SP) = Rs. 2550

Profit = SP - CP

= 2550 - 1500

= 1050

Percentage Profit = Profit/CP × 100

= 1050/1500 × 100

= 0.7 × 100

= 70%

Explanation

Given expression: 1830 + 20 × 50 - 396 ÷ 3

Following order of operations:

1. Multiplication: 20 × 50 = 1000

2. Division: 396 ÷ 3 = 132

3. Now, the expression becomes:

1830 + 1000 - 132

= 1830 + 1000 = 2830

= 2830 - 132 = 2698

Explanation

Given logx (4/9) = 2

This can be rewritten as:

x² = 4/9

Taking the square root of both sides:

x = ±√(4/9)

x = ±2/3

Since the base of a logarithm is typically positive, we consider x = 2/3.

Explanation

Let's solve the equation:

4/5 (x + 7) = 3(2x - 7)

Multiply both sides by 5 to eliminate the fraction:

4(x + 7) = 15(2x - 7)

Expand both sides:

4x + 28 = 30x - 105

Subtract 4x from both sides:

28 = 26x - 105

Add 105 to both sides:

133 = 26x

Divide both sides by 26:

x = 133/26