Explanation

Given equation:

x - 4 = 21(1/x)

Multiply both sides by x:

x² - 4x = 21

Rearrange the equation:

x² - 4x - 21 = 0

Factor the quadratic equation:

(x - 7)(x + 3) = 0

Solve for x:

x = 7 (since x is a positive number)

Explanation

0.5 × 0.06 = 0.03

Explanation

To find the farthest number from -1 on the number line:

-1 is the reference point.

-10 is 9 units away from -1.

10 is 11 units away from -1.

5 is 6 units away from -1.

Since 10 is the farthest (11 units away), the correct answer is: 10

Explanation

To find the arrival time, add 5 hours and 30 minutes to the departure time:

Departure time: 21:15 PM (Wednesday)

Add 5 hours: 02:15 AM (Thursday)

Add 30 minutes: 02:45 AM (Thursday)

The correct answer is: 2:45 AM on Thursday

Explanation

Let's denote the denominator as x. Then, the numerator is x - 5.

Original fraction: (x - 5)/x

After adding 1 to both numerator and denominator:

New fraction: (x - 5 + 1)/(x + 1) = (x - 4)/(x + 1)

Given that the new fraction is 2/3:

(x - 4)/(x + 1) = 2/3

Cross-multiply:

3(x - 4) = 2(x + 1)

Expand and solve:

3x - 12 = 2x + 2

x = 14

So, the original fraction is:

(x - 5)/x = (14 - 5)/14 = 9/14

Explanation

Given that one number is two-thirds of the second:

x = (2/3)y

The sum of the two numbers is 45:

x + y = 45

Substitute x from the first equation:

(2/3)y + y = 45

Combine like terms:

(5/3)y = 45

Multiply both sides by 3:

5y = 135

Divide by 5:

y = 27

Now, find the smaller number x:

x = (2/3)y

x = (2/3) × 27

x = 18

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

To find the nth term, replace n with n+3:

an = 2(n+3) - 5

an = 2n + 6 - 5

an = 2n + 1

Therefore, the nth term is: 2n + 1

Explanation

Total weight increased is 1.5 * 10 = 15.

So weight of new person is 45+15 = 60

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)