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avanturin [10]
3 years ago
7

14. Michelle simplified an expression for the perimeter of the rectangle below and got X + 35.

Mathematics
1 answer:
Zigmanuir [339]3 years ago
6 0

Answer:

The correct expression for the perimeter is P=(\frac{5}{3}x+70)\ units

see the explanation

Step-by-step explanation:

The complete question in the attached figure

Let

L ----> the length of rectangle

W ---> the width of rectangle

we know that

The perimeter of rectangle is equal to

P=2(L+W)

In this problem we have

L=(\frac{5}{6}x+23)\ units

W=12\ units

substitute the values

P=2(\frac{5}{6}x+23+12)

P=2(\frac{5}{6}x+35)

P=(\frac{10}{6}x+70)\ units

Simplify

P=(\frac{5}{3}x+70)\ units

so

Michelle didn't multiply the sum of length and width by 2

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<h3>Answer:  They're all the same</h3>

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Reason:

2^6 means we have 6 copies of "2" multiplied out as shown in choice B. That explains how A and B are the same, and we can say

2^6 = (2*2*2)*(2*2*2)

The parenthesis are optional, but I find they're handy to count the '2's easier.

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Now notice that

2^3 = 2*2*2

So,

2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2^3)*(2^3)\\\\2^6 = (2^3)^2\\\\

The last step is possible because we have two copies of 2^3 multiplied together.

This shows that choice C is equivalent to A and B.

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Lastly,

2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2*2)*(2*2)*(2*2)\\\\2^6 = (2^2)*(2^2)*(2^2)\\\\2^6 = (2^2)^3\\\\

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This shows choice D is equivalent to the others.

All four expressions are the same.

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