Explanation

Given:

xy = 35

x + y = 12

To find x² + y²:

(x + y)² = x² + 2xy + y²

144 = x² + 2(35) + y²

144 = x² + 70 + y²

x² + y² = 144 - 70

= 74

Explanation

The idiom donkey's year means something that is continued for a very long time.

Explanation

"To take a rain check" means to decline an offer for now but suggest doing it later.

It originally comes from sports tickets being reused when events were rained out.

Explanation

Given:

3x : 2y = 6 : 5

Cross-multiply:

(3x) × 5 = (2y) × 6

15x = 12y

Divide both sides by 3y:

5x/y = 4

x/y = 4/5

So, x : y = 4 : 5

Explanation

Given:

Initial value = 80

Final value = 80

Percentage increase = ((Final - Initial) / Initial) × 100

= ((80 - 80) / 80) × 100

= (0 / 80) × 100

= 0%

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18

Explanation

Given equation:

3/x + 2/(x+1) = 1

Multiply both sides by x(x+1):

3(x+1) + 2x = x(x+1)

Expanding both sides:

3x + 3 + 2x = x² + x

Combine like terms:

5x + 3 = x² + x

Rearrange the equation:

x² - 4x - 3 = 0

Solve the quadratic equation:

x = (4 ± √(16 + 12)) / 2

x = (4 ± √28) / 2

x = (4 ± 2√7) / 2

x = 2 ± √7

The answer is 2 + √7 or 2 - √7.

Explanation

Let's denote A's rate of work as A, and B's rate of work as B.

Given A + B together complete the work in 12 days:

(A + B)'s 1 day's work = 1/12

B alone completes the work in 20 days:

B's 1 day's work = 1/20

A's 1 day's work = (A + B)'s 1 day's work - B's 1 day's work

= 1/12 - 1/20

= (5 - 3) / 60

= 2 / 60

= 1 / 30

A alone will complete the work in 30 days.

Explanation

Explanation

The standard rate of Zakat on silver, gold, and currency is 2.5% (or 2 ½ %)

........

Zakat money can be spent on Poor Muslims

Zakat became obligatory in 2 AH

List of Heads of Zakat

1. Al-Fuqara (The poor)

2. Al-Masakin (The needy)

3. Zakat collectors

4. Who converted to Islam

5. Freeing captives

6. Debtors

7. In the path of Allah

8. Wayfarer (Traveler)