Need help with these please---

2. A long distance phone company has a monthly fee of $7.95 and charges a rate of $0.05 per minute. Another long distance company has a monthly fee of $9.95 and charges a rate of $0.03 per minute. At how many minutes would the two companies have equal charges?

15. A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of the boat in still water.

20. Solve: 5x^2 - 10x = 0

50. (x-1)(x^3 + x^2 + x) =?

Thanks
-MC

2. Let x = minutes

7.95 + .05x = 9.95 + .03x

Solve for x.

15. Can't help here.

20. 5x(x-2) = 0

x = 0 or 2

50. Do you want to factor or multiply?

2. To find the number of minutes at which the two companies have equal charges, we can set up an equation. Let's assume that the number of minutes is represented by 'x'.

For the first long distance company, the charges can be calculated as follows: monthly fee + (rate per minute * number of minutes) = $7.95 + ($0.05 * x)

For the second long distance company, the charges can be calculated as follows: monthly fee + (rate per minute * number of minutes) = $9.95 + ($0.03 * x)

To find the number of minutes at which the charges are equal, we can set up the equation:

$7.95 + ($0.05 * x) = $9.95 + ($0.03 * x)

By simplifying this equation and solving for 'x', you will find the number of minutes at which the two companies have equal charges.

15. The rate of the boat in still water can be found using the concept of relative speed.

Let's assume the rate of the boat in still water is 'b' and the rate of the current is 'c'.

For the upstream journey, the effective speed of the boat can be calculated as b - c (since the boat is moving against the current), and the time taken is 4 hours.

For the downstream journey, the effective speed of the boat can be calculated as b + c (since the boat is moving with the current), and the time taken is 2.5 hours.

Using the formula distance = speed * time, we can set up two equations:

30 = (b - c) * 4
30 = (b + c) * 2.5

Solving these two equations simultaneously will give you the rate of the boat in still water.

20. To solve the equation 5x^2 - 10x = 0, we can start by factoring out the common factor:

5x(x - 2) = 0

Since the product of two numbers is zero if and only if at least one of the numbers is zero, we set each factor equal to zero:

1. 5x = 0
This gives us x = 0 as one solution.

2. x - 2 = 0
This gives us x = 2 as another solution.

So, the equation has two solutions: x = 0 and x = 2.

50. To simplify the expression (x-1)(x^3 + x^2 + x), we can use the distributive property of multiplication over addition/subtraction.

First, distribute (x-1) to each term inside the parentheses:

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

Now, simplify each term:

= x^4 + x^3 + x^2 - x^3 - x^2 - x

Combine like terms:

= x^4 - x

So, the simplified expression is x^4 - x.