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Pepsi [2]
3 years ago
7

the length of a rectangle is 3 units shorter than one -third of the width, x. Which expression represents the perimeter of the r

ectangle? A) 8/3x-6, B) 2/3x -4, C) 2/3x -8, D) 8/3x -2.​
Mathematics
1 answer:
Mariana [72]3 years ago
8 0

Answer:

A) \frac{8}{3} x - 6

Step-by-step explanation:

Let the width of the rectangle be x units.

\therefore \: length \: of \: rectangle =  \frac{1}{3} x - 3 \\ Perimeter \: of \: rectangle  = 2(l + w) \\  = 2  \bigg( \frac{1}{3} x - 3 + x \bigg)\\  = 2  \bigg( x + \frac{1}{3} x - 3 \bigg)\\  = 2  \bigg(  \frac{3x + x}{3}  - 3 \bigg)\\  = 2  \bigg(  \frac{4x}{3}  - 3 \bigg) \\  = 2  \bigg(  \frac{4x}{3}  - 3 \bigg) \\  =   \frac{2 \times 4x}{3}  -2 \times  3  \\  \purple{ \bold{{Perimeter \: of \: rectangle   =  \frac{8}{3} x - 6}}}

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Step-by-step explanation:

lets do a table!

cherry | blueberry

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When there are 2 blueberry, there are 3 cherry. 3 is 1 more than 2. When there are 4 blueberry, there are 6 cherry. 6 is 2 more than 4. When there are 6 blueberry, there aare 9 cherry. 9 is 3 more than 6.

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We also know that
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2. Only the contrapositive is logically equivalent to the original statement.
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Now back to the given statement.
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Original statement
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contrapositive of 
<span>
"If an item is not worth five dimes, then it is not worth two quarters.”
is the negation of the converse, which become
"If an item is worth two quarters, then it is worth (at least) five dimes."


The converse of the previous statement is therefore
"If an item is worth (at least) five dimes then it is worth two quarters"

In this particular case, we can also take advantage of the fact that the contrapositive is the negation of the converse.  So all we have to do is the provide the negation of each component of the contrapositive to get the converse:
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as before.

Note that the converse does NOT logically mean the same as the original statement.

</span>
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