Markup = Principal × Rate × Time
= 8000 × 7/100 × 5
= 8000 × 0.07 × 5
= 8000 × 0.35
= 2800
(x + 3)(x + k) = x^2 + kx + 3x + 3k
= x^2 + (k + 3)x + 3k
No linear term means k + 3 = 0
So, k = -3
The given ratio is:
5:10 :: 5:x
This is a proportion, so we can set up an equation:
5/10 = 5/x
Cross-multiply:
5x = 5 × 10
5x = 50
Divide by 5:
x = 50/5
x = 10
Let x be the number of years in the future. Then:
Father’s age = 41 + x, Son’s age = 9 + x
Set up the equation: 41 + x = 3(9 + x)
→ 41 + x = 27 + 3x → 14 = 2x → x = 7 years.
This is a statement of the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
It ensures the sides form a valid triangle.
To solve the equation:
75 - 9t = 5(-4 + 2t)
Expand the right-hand side:
75 - 9t = -20 + 10t
Add 9t to both sides:
75 = -20 + 19t
Add 20 to both sides:
95 = 19t
Divide by 19:
t = 95/19
t = 5
Let the younger sister's present age be x.
Fareeha's present age = x + 4
After 10 years:
Younger sister's age = x + 10
Fareeha's age = x + 4 + 10 = x + 14
Given:
x + 10 + x + 14 = 48
2x + 24 = 48
2x = 24
x = 12
= 12 + 4
= 16 years
= 8/3 - 3/4
= LCM of 3 and 4 = 12
= 8/3 = 32/12, 3/4 = 9/12
= 32/12 - 9/12 = 23/12
(16 ÷ 80) × 100 = 20%
It shows that 16 is 20% of 80.
∪ = {1, 2, 3, ..., 15}
A = {2, 4, 6, ..., 14}
B = {1, 3, 5, ..., 15}
A' = ∪ - A = {1, 3, 5, ..., 15} = B
B' = ∪ - B = {2, 4, 6, ..., 14} = A
A' ∪ B' = B ∪ A = ∪ (since B and A are complementary sets that together form ∪)