Explanation

You're given:

2a – 3b = 10

To find:

(2a – 3b)³

This is straightforward:

(2a – 3b)³ = (10)³ = 1000

Explanation

Let daughter's age = x  

Then father’s age = 47 - x  

4 years ago:  

Father's age = 47 - x - 4 = 43 - x  

Daughter's age = x - 4

Given: Father was twice the daughter's age 4 years ago  

43 - x = 2(x - 4)  

43 - x = 2x - 8  

43 + 8 = 3x ⇒ 51 = 3x ⇒ x = 17

Explanation

Given:  

(2/7)x + 12 = 30 - 3  

(2/7)x + 12 = 27  

(2/7)x = 15  

Multiply both sides by 7:  

2x = 105 ⇒ x = 52.5

Explanation

Given:  

a/3 = b/2

Cross-multiply:  

2a = 3b → a = (3b)/2

Now plug this value of a into the expression:

(2a + 3b) / (3a - 2b)  

= [2(3b/2) + 3b] / [3(3b/2) - 2b]  

= (3b + 3b) / (9b/2 - 2b)  

= 6b / [(9b - 4b)/2]  

= 6b / (5b/2)  

= 6b × (2/5b) = 12/5

Explanation

To find the value of 4x + 2y, we can multiply the given equation 2x + y = 5 by 2.

Multiplying both sides by 2 gives:

4x + 2y = 2(5)

4x + 2y = 10

So, the correct answer is: 10

Explanation

Sum of the 5 number = -10 * 5 = -50

Sum of the 3 numbers = 16

Sum of other 2 numbers = -50 - 16 = -66

Average of the 2 numbers = -66/2 = -33.

Explanation

a + b = 3(c + d)

We need to find the average of a, b, c, and d, which is:

(a + b + c + d) / 4

Substitute a + b from the given equation:

= [3(c + d) + c + d] / 4  

= [4(c + d)] / 4  

= c + d

Explanation

V = π × r² × L  

= π × 3² × 10  

= π × 9 × 10 = 90π cm³

Explanation

Given:

- 40 animals  

- Each animal needs 20 packets of milk  

- 1 packet = 200 ml  

- Milk cost = 4.6 pesos per litre  

- Only 80% of milk is provided  

Step 1: Total packets needed

40 animals × 20 packets = 800 packets

Step 2: Total milk in ml

800 packets × 200 ml = 160,000 ml

Step 3: Convert to litres

160,000 ml ÷ 1000 = 160 litres

Step 4: Only 80% is provided

160 litres × 0.8 = 128 litres

Step 5: Total cost

128 litres × 4.6 pesos = 588.8 pesos

Explanation

To convert 158°F to Celsius (°C), use the formula:

°C = (°F − 32) × 5/9

°C = (158 − 32) × 5/9  

= 126 × 5/9  

= 630 / 9 = 70°C