I believe x=3.
4x-3(-2)=18
4x=12
x=3
Yes 1,120 gallons per week (7 days)
Just divide 800 by 5 and see that the sprinkler system uses 160 gallons a day. Multiply 160 by 7 for the amount used a week and you will find that the answer is 1,120 gallons of water.
4+8 is 12 so yes it is correct!!!
The function for the height is

f(0) = 5 cos(0) + 7 = 5 + 7 = 12 (verified)
The period is T = 12 hours.
After 4 hours (t = 4), the height is

A graph of f(t) confirms the answer.
Answer: 4.5 ft