On monday, elsbeth’s bank account balance was -$16.75. on tuesday, she deposited a check for $5.72. on thursday, she deposited $16.75. what is her new balance?

-16.75 + (5.72 + 16.75)

use the commutative property to get:

-16.75 + (16.75 + 5.72)

use the associative property to get:

(-16.75 + 16.75) + 5.72

on friday, elsbeth deposited her pay check for $872.56. what was the account’s final total?
a. -$866.84
b. $878.28
c. $895.03
d. $903.10

$5.72 - Thursday's balance

$878.28 - Final total

Step-by-step explanation:

Commutative property - States that you can move numbers around without affecting the sum.

-16.75 + 5.72 + 16.75

5.72 - 16.75 + 16.75                                = $5.72

5.72 + 16.75 - 16.75

Associative property - States that you can regroup numbers without affecting the sum.

-16.75 + (5.72 + 16.75)

(-16.75 + 5.72) + 16.75                              =$5.72

$5.72 + $872.56  = $878.28

~Hope this helps!~

(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