First we need to know both the formula of A and B.

The formula of A is
C = 5 + 0.25p
with C representing total cost and p representing the amount of checks.

The formula of B is
C = 6 + 0.15p
with C representing total cost and p representing the amount of checks.

To find the point where A and B cost the same, we solve the following equation:
5 + 0.25p = 6 + 0.15p

Collecting terms gives us
-1 = -0.1p

Now we have to divide by -0.1 and we get.
10 = p
p = 10

So our answer: after 10 checks both accounts cost the same amount of money. Answer A.

7 0

2 years ago

(4,7,12,19) How do you right this in recursive and explicit equations??????? pls help

Soloha48 [4]

You can see how the difference between two consecutive terms is constantly increasing:

$a_1 = 4$

$a_2 = 7 = 4+3$

$a_3 = 12 = 7+5$

$a_4 = 19 = 12+7$

So, for the next terms we'll have to add +9, +11, +13 and so on.

Also, note that $a_2$ is obtained by adding the 2nd odd number to $a_1$ , $a_3$ is obtained by adding the 3rd odd number to $a_2$ , and so on.

So, the recursive formula is

$a_n = a_{n-1}+(2n-1),\quad a_1=1$

For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have

$a_n = n^2+3$