Given A = {x | x ∈ P ∧ 5 ≤ x ≤ 13}, where P is the set of prime numbers:
The prime numbers between 5 and 13 are 5, 7, 11, and 13.
So, A = {5, 7, 11, 13}, which has 4 elements.
The power set P(A) has 2^n elements, where n is the number of elements in A:
2^4 = 16
Given the equations:
x + 3y = 53 ... (1)
4x - 2y = 2 ... (2)
We can solve these equations using substitution or elimination. Let's use elimination.
Multiplying equation (1) by 2 and equation (2) by 3 to eliminate y:
2x + 6y = 106
12x - 6y = 6
Adding both equations:
14x = 112
x = 8
To find z1z2:
z1 = 6 + 3i
z2 = 3 - 5i
z1z2 = (6 + 3i)(3 - 5i)
= 18 - 30i + 9i - 15i^2
= 18 - 21i + 15 (since i^2 = -1)
= 33 - 21i
The area of a trapezium is given by:
Area = (1/2) × (sum of bases) × altitude
Given:
Area = 153 m^2
Altitude = 9 m
One base = 13 m
Let's denote the other base as 'b'. Then:
153 = (1/2) × (13 + b) × 9
Multiply both sides by 2:
306 = (13 + b) × 9
Divide both sides by 9:
34 = 13 + b
Subtract 13 from both sides:
b = 21
x + 1/x = 10
Squaring both sides:
(x + 1/x)^2 = 10^2
x^2 + 2(x)(1/x) + 1/x^2 = 100
x^2 + 2 + 1/x^2 = 100
Subtract 2 from both sides:
x^2 + 1/x^2 = 98
The cube of 12 is:
12 × 12 × 12 = 1728
144 = 2 × 2 × 2 × 2 × 3 × 3, which simplifies to 2⁴ × 3².
This is the correct prime factorization, using only prime numbers.
The odd numbers between 10 and 18 are 11, 13, 15, and 17.
These are the elements that satisfy the given set condition.
A number divisible by 9 but not by 18 must be divisible by 9 but not by 2 (since 18 is a multiple of 2 and 9).
27 is divisible by 9 but not by 18, as 27 ÷ 9 = 3, but 27 ÷ 18 does not result in an integer.
Khadija is thrice as old as her daughter, so:
K = 3D
The sum of their ages is 45:
K + D = 45
3D + D = 45
4D = 45
D = 45/4
D = 11.25 (12)
Get instant updates and alerts directly from our site.
Install this app on your device for quick access right from your home screen.
