Given:
x² - y² = 28
x - y = 8
Factor the first equation:
(x - y)(x + y) = 28
Substitute x - y = 8:
8(x + y) = 28
Divide by 8:
x + y = 28/8
x + y = 3.5
The average of x and y is:
(x + y)/2 = 3.5/2 = 1.75
If two circles touch internally, the distance between their centers is the difference of their radii: r₁ - r₂.
r₁ is the radius of the larger circle, and r₂ is the radius of the smaller circle.
If the sum of the radii equals the distance between the centers, the circles touch externally.
Original cost price = 100
Original selling price = 100 + 320% of 100 = 420
New cost price = 100 + 25% of 100 = 125
Since the selling price remains constant, the profit is:
Profit = Selling price - New cost price = 420 - 125 = 295
Percentage of selling price that is profit:
(295 / 420) * 100% ≈ 70%
So, the correct answer is 70%.
Finding the pattern:
6−4=2
9−6=3
13−9=4
The differences between consecutive numbers are +2, +3, +4.
Following this pattern, the next difference should be +5.
So,
13+5=18.
a-b=9 square both sides
(a-b)2=9
(a-b)2=(9)2
A2-B2-2ab=81
A2-B2-2(3)=81
A2-B2=81+6
A2-B2=87
3/4 = 0.75
The pattern of the series is obtained by adding 2, 2, 4, 18, ... (doubling the previous increment and adding 2).
2 + 2 = 4
4 + 2 = 6
6 + 4 = 10
10 + 18 = 28
28 + 54 = 82
8 years ago, Hyder's age was x - 8.
7 years from now, Hyder's age will be x + 7.
According to the problem:
x + 7 = 2(x - 8)
Simplify the equation:
x + 7 = 2x - 16
Add 16 to both sides:
x + 23 = 2x
Subtract x from both sides:
23 = x
