Karen and Maria each open a savings account at the same time. They only make deposits into their accounts and do not make withdrawals. When Karen opens her account she deposits $28 into it. She then deposits $5 into her account each week. The total amount of money (y), in dollars, in Maria’s account x weeks after it is opened is described by the function y=8x+7. What is the total amount of money that each girl has in her account 2 weeks after they have the same amount of money in their accounts?

The amount in Maria's account is $79.

The amount in Karen's account is $73.

Step-by-step explanation:

Karen deposits $28 into her account and she deposits $5 each week into her account.

From this given information, the equation can be framed as y = 28+5x (1)

where,

The equation for Maria's account is given as y = 7+8x (2)

To find the no.of weeks at which they both have same amount of money :

Equating the equations (1) and (2),

⇒ 28 + 5x = 7 + 8x

⇒ 28-7 = 8x-5x

⇒ 21 = 3x

⇒ x = 21/3

⇒ x = 7 weeks

After 7 weeks, the money in the account of Karen & Maria will be same.

To find the amount of money in each girl's account after 2 weeks :

It is given that, you have to calculate amount of money that each girl has in her account 2 weeks after they have the same amount of money in their accounts.

We already know that, it takes 7 weeks for them to have same amount.

So, 7 weeks + 2 weeks = 9 weeks

You have to calculate the amount in each girl's account after 9 weeks.

Karen's account :

Substitute x=9 in eq(1),

⇒ y = 28+5(9)

⇒ y = 28+45

⇒ y = 73

The amount in Karen's account is $73.

Maria's account :

Substitute x=9 in eq(1),

⇒ y = 7+8(9)

⇒ y = 7+72

⇒ y = 79

The amount in Maria's account is $79.

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.