Explanation

Explanation

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

Explanation

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.

Explanation

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%.

Explanation

Explanation

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.

Explanation

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

Explanation

3/4 = 0.75

Explanation

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

Explanation

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