Help please!! Worth 14 points!

6 days

Step-by-step explanation:

Hi there!

Let d be equal to the number of days that pass.

1) Form expressions

We're told that our sister earns $30 a day, but needs to pay $60 at first:

We're also told that we earn $20 a day:

2) Form an equation

We're solving for the number of days that pass (d) in order for both our and our sister's income to equal each other.

For our income and our sister's income to equal each other, the following must be true:

Because the only variable here is d, we can simply isolate it to determine the number of days that would pass.

3) Solve for d

Subtract 30d from both sides to isolate d on one side

Divide both sides by -10 to isolate d

Therefore, for both our income and our sister's income to become equal, 6 days would pass.

I hope this helps!

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50