The number of gallons g in a swimming pool being filled with water is g = 50x + 1,000, where x is the number of hours since sunrise. It has been 10 hours since sunrise. What is the initial value?
To find the initial value, we need to find the value of g when x is 0.
Substitute x = 0 into the equation:
g = 50(0) + 1,000
g = 0 + 1,000
g = 1,000
Therefore, the initial value is 1,000 gallons.
Days Fine
2 30 cents
3 45 cents
4 60 cents
The table shows the fine owed for an overdue library book according to how many days it is overdue. What is the initial value?
To find the initial value, we need to find the fine when there are 0 days overdue.
From the given table, we see that when there are 0 days overdue, the fine is not mentioned. We cannot determine the initial value based on this information alone.
Days Fine
2 30 cents
3 45 cents
4 60 cents
The table shows the fine owed for an overdue library book according to how many days it is overdue. What is the initial value?
__ cents
To find the initial value, we need to find the fine when there are 0 days overdue.
From the given table, we can see that when there are 2 days overdue, the fine is 30 cents.
Since there is a linear relationship between the number of days overdue and the fine, we can assume that the fine increases by a constant amount per day.
To find this constant amount, we can find the difference in fines between two consecutive days:
45 cents - 30 cents = 15 cents
So, the fine increases by 15 cents per day overdue.
To find the fine when there are 0 days overdue, we can subtract the constant amount from the fine when there are 2 days overdue:
30 cents - 15 cents = 15 cents
Therefore, the initial value is 15 cents.
Years Amount
1 $1,080
2 $1,160
3 $1,240
The table shows the amount of money in a bank account after a certain number of years. What is the initial?
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To find the initial amount, we need to find the amount of money in the bank account when there are 0 years.
From the given table, we can see that when there are 1 year, the amount is $1,080.
Since there is a linear relationship between the number of years and the amount, we can assume that the amount increases by a constant amount per year.
To find this constant amount, we can find the difference in amounts between two consecutive years:
$1,160 - $1,080 = $80
So, the amount increases by $80 per year.
To find the amount when there are 0 years, we can subtract the constant amount from the amount when there is 1 year:
$1,080 - $80 = $1,000
Therefore, the initial amount is $1,000.
Victor will start paying off his credit card in January. He uses the function f (x) = - 35x + 2,500 to model the amount of money he owes x months after January. How much money does he owe at the beginning of January.
$ __
To find out how much money Victor owes at the beginning of January, we need to find the value of f(x) when x is 0 (since x represents the number of months after January).
Substitute x = 0 into the function:
f(0) = -35(0) + 2,500
f(0) = 0 + 2,500
f(0) = 2,500
Therefore, Victor owes $2,500 at the beginning of January.
Cesar rents a bicycle for a flat rate plus $10 per hour. He models the cost of the rental with the function f (x) = 10x + 15, where x is the number of hours he rents the bicycle, and f (x) is the total cost of the bicycle rental, including the flat rate and the hourly fee. What is the flat rate for the bicycle rental?
$ __