Explanation

Let z = 4y-1

When x = 14, y = 2, z = (4*2) – 1 = 7

Now, x varies directly as z = 4y-1

When y = 5, z = (4*5) – 1 = 19

x 14 7

y - 19

Therefore, x = (14*19)/7 = 38

Explanation

The sum of the interior angles of a triangle is 180 degrees.

x-35 + x-25 + 1/2x - 10 = 180

2.5x -70 = 180

2.5x = 250

x=100

Explanation

ND16-3-2023

Explanation

Explanation

5 (as 9^n - 4^n is a difference of two odd powers, which is always divisible by 5)

13 (as 9^n - 4^n can be rewritten as (13-4)^n - 4^n, which is always divisible by 13)

Explanation

Initial volume of water = (3/4) × 4 × 2 × 4.8 = 14.4 m³

Initial depth of water = (14.4 m³) / (4 × 2) = 3.6 m

Additional water = 4000 liters = 4 m³

New volume of water = 14.4 m³ + 4 m³ = 18.4 m³

New depth of water = (18.4 m³) / (4 × 2) = 4.6 m then subtract the initial height of the water from the total height of the tank 4.8m - 4.6m = 0.2m + 3.6m = 3.8m then add the additional depth 3.8m + 0.3m = 4.1m

Therefore, the depth of water in the tank is: 4.1 m

Explanation

Explanation

 Increase 9,000 by 30%, which is the same as increasing by three tenths (3/10).

30% more than 9,000 is

11,700

Explanation

A general partnership is a business made up of two or more partners, each obligated for the business's debts, liabilities, and assets.

Partners assume unlimited liability, potentially subjecting their personal assets to seizure if the partnership becomes insolvent.

ND5-09-2023

Explanation

The trade-off theory of capital structure tells us that:

Managers should seek an optimal mix of equity and debt that minimizes the firm's weighted average cost of capital,

which in turn maximizes company value

ND4-09-2023