Explanation

Initial population in 2015 = 1400  

Decrease rate = 6% per year → so each year 94% remains

For exponential decay:  

P = Initial × (1 - rate)^t  

Here rate = 6% = 0.06  

So 1 - 0.06 = 0.94

Therefore, the exponential decay equation is P = 1400(0.94)ᵗ.

Last verified on 28-07-2026

Explanation

Boys = 14  

Girls = 18  

Ratio of girls to boys = girls : boys = 18 : 14  

Simplify by dividing both by 2:  

18 : 14 = 9 : 7

Last verified on 28-07-2026

Explanation

The wall = 4 m high  

Distance from wall = 3 m  

Ladder = hypotenuse

Use Pythagoras theorem:  

c² = a² + b²  

c² = 3² + 4²  

c² = 9 + 16  

c² = 25  

c = √25 = 5

Last verified on 28-07-2026

Explanation

If y is directly proportional to x, then:  

y = kx, where k is the constant of proportionality

Given x = 2, y = 5:  

5 = k _ 2  

k = 5/2

Now find y when x = 7:  

y = (5/2) _ 7  

y = 35/2

Last verified on 28-07-2026

Explanation

Multiply 2 × 3 = 6.

Count the decimal places (3 + 2 = 5), so the answer is 0.00006.

Last verified on 28-07-2026

Explanation

Given:  

5x/4 = 8y/3

Cross multiply:  

5x _ 3 = 8y _ 4  

15x = 32y

Now write as ratio x : y  

x / y = 32 / 15  

So x : y = 32 : 15

Last verified on 27-07-2026

Explanation

√2 is an irrational number because it cannot be written as a fraction.

√9 = 3, 8, and 9 are all rational numbers.

Last verified on 27-07-2026

Explanation

Volume of cube = side³

Side = ∛Volume = ∛275.

Last verified on 27-07-2026

Explanation

2x + 4x = 3 − 15

6x = −12, therefore x = −2.

Last verified on 27-07-2026

Explanation

The degree of a polynomial = the highest power of x.

In 2kx² − x + 1:  

2kx² has x² → power 2  

x has x¹ → power 1  

1 has x⁰ → power 0

Highest power = 2

Last verified on 27-07-2026