Describe the total change to Ms. Thomas' savings account balance after making six monthly payments on her car loan. Model your answer using a number sentence.

$-1465.5

Step-by-step explanation:

Complete question

Every month, Ms. Thomas pays her car loan through automatic payments (withdrawals) from her savings account. She pays the same amount on her car loan each month. At the end of the year, her savings account balance changed by −$2,931 from payments made on her car loan. Describe the total change to Ms. Thomas’ savings account balance after making six monthly payments on her car loan. Model your answer using a number sentence.

Given the following

Savings balance (after 1 year) =

−$2,931

If she pays the same amount on her car loan each month, we are to find the total change to Ms. Thomas’ savings account balance after making six monthly payments on her car loan, this can be expressed as;

$x = 6months savings

Solving both equalities

Savings balance (after 1 year) =

−$2,931

Since 1year = 12months

-$2,931 =12months savings

$x = 6months savings

To get the total savings after 6months we will find x by cross multiplying;

12×x = -2931×6

Divide through by 12

12x/12 = (-2931×6)/12

x = -2931/2

x = -1465.5

Hence Ms. Thomas' savings account balance after making six monthly payments on her car loan is $-1465.5

i would need to see the dot plot : )

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240