Ms. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one set of parentheses. 4
(
3
x
+
5
y
+
2
z
)
+
3
(
x
−
z
)
4(3x+5y+2z)+3(x−z)

• Tom wrote
12
x
+
20
y
+
8
z
12x+20y+8z

• Jenna wrote
5
(
3
x
+
4
y
+
z
)
5(3x+4y+z)

• Chris wrote
15
x
+
20
y
−
5
z
15x+20y−5z

Which, if any, of the three students wrote an expression that is equivalent to Ms. Peterson’s expression?

Answer wrote an equivalent expression.
Show your work to prove which expressions, if any, are equivalent.

b and c

step-by-step explanation:

(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

do have an equation or graph or

step-by-step explanation:

hi,

the area of abcd is 245.

3*24=230

4*94=1039

2*12=24

add all of them up, you get 2450