Takuya's parents gave him $100 dollars as a birthday gift. Since he loves board games, he spent $20 out of his present on board games at the end of each month until his money ran out.

Let f(n) be the amount of money that remained from Takuya's present during month n where n=1 represents the month he received his present.

f is a sequence. What kind of sequence is it?

The expression that represents the amount of money Takuya has over the months is "f(n) = f(1) + (n - 1)*r" and the sequence is an arithmetic sequence.

Step-by-step explanation:

Since the initial amount of money Takuya had was 100 dollars and he spent 20 dollars every month, then each element of the sequence is related to it's prior by the sum of -20, therefore it's a arithmetic sequence. In order to calculate the "nth" term of a sequence like this we need to apply the following formula:

f(n) = f(1) + (n-1)*r

f = {100, 80, 60, 40, 20, 0}

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

it would take 7/10 of an hour too fill the pool.

step-by-step explanation: