A power set contains all possible subsets of a given set, including the empty set and the set itself.
Example: If set = {a, b}, then power set = {∅, {a}, {b}, {a, b}}.
Let's factor:
x^2 - y^2 = (x + y)(x - y)
x^2 - xy = x(x - y)
The common factor is (x - y).
To evaluate 2(-7)²:
First, calculate the exponent:
(-7)² = (-7) × (-7) = 49
Now, multiply by 2:
2 × 49 = 98
4 boys ran 60km each in 6 hours,10km distance covered by 1 boy in 1 hour
Given that the two sides of the isosceles triangle are equal:
3x - 2y + 2 = x - y + 7
This simplifies to:
2x - y = 5
The sum of the two equal sides is 12 cm:
(3x - 2y + 2) + (x - y + 7) = 12
4x - 3y = 3
Solving these two equations simultaneously, we find x = 6.
In the term x², the coefficient is the number multiplying the variable.
Since nothing is written explicitly, the coefficient is understood to be 1.
Given x = 1 is a solution, let's find 'a':
a(1)² + 5(1) - 3 = 0
a + 2 = 0
a = -2
The equation is -2x² + 5x - 3 = 0.
Let's factor or solve:
-2x² + 5x - 3 = 0
-2x² + 2x + 3x - 3 = 0
-2x(x - 1) + 3(x - 1) = 0
(-2x + 3)(x - 1) = 0
x = 1 (given) or x = 3/2
The other solution is x = 3/2.
The trigonometric identity is:
1 + cot²θ = csc²θ
If b² - 4ac < 0, the discriminant is negative, meaning the quadratic equation has complex (imaginary) roots.
These roots are conjugate pairs and unequal.