0.5x + 5 = x - 0.75
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.
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)
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).
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
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%
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
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.
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