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bearhunter [10]

3 years ago

13

Katie cut out a rectangular piece of wrapping paper that was 2 times as long and 3 times as wide as the box that she was wrappin

g. the box was 5inches long and 4 inches wide. what is the perimeter of the wrapping paper that katie cut?

1 answer:

kotegsom [21]3 years ago

3 0

2*5=10 (the measure of one long side is 10)
3*4=12 (the measure of one wide side is 12)

A box has four sides to the perimeter of the flat wrapping paper must consist of four edges. Because we know that one edge is 10 inches long and another side is 12 inches wide we assume that the corresponding sides are equal.

So now we know that we have two sides that are 10 inches and 2 sides that are 12 inches.

10+10+12+12= 44 inches

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What is the solution of ?<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20x-7%3D%5Cfrac%7B3%7D%7B4%7D%20x%2B14" id="Tex

Nonamiya [84]

Combine the terms by multiplying into a single fraction.

$\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }$

Find the common denominator.

$\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }$

Combine the multiplied terms into a single fraction

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }$

Find the common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }$

Eliminate the denominators of the fractions.

$\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }$

Cancel the multiplied terms that are in the denominator.

$\bf{2(5x-14)=3x+56}$

To distribute.

$\bf{10x-28=3x+56 }$

Add 28 to both sides.

$\bf{10x-28+28=3x+56+28 }$

Simplify

$\bf{10x=3x+84 }$

Subtract 3x from both sides.

$\bf{10x-3x=3x+84-3x }$

Simplify

$\bf{7x=84 }$

Divide both sides by the same factor.

$\bf{x=\dfrac{84}{7} }$

Simplify

$\bf{x=12 \ \ \ === > \ \ \ Answer}$

↓

<h3>Verification</h3>

Let x=12.

$\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3\times12}{4}+14 }$
$\bf{30-7=\dfrac{36}{4}+14 }$
$\bf{30-7=9+14 }$
$\bf{23=9+14 }$
$\bf{23=23}$

Checked ✅

3 0

2 years ago

PLEASE HELP IM CONFUSED! Find what the measurements of angles a-c are and state the reason

nata0808 [166]

Answer:

<a = 90° (180-90 supplementary angle)

<b = 90° (180-90 supplementary angle)

<d = 48° (180-132 supplementary angle)

<e = 132° (opposite angle)

<c = 42° (interior angles of a triangle equal 180. 180-48-90=42)

Step-by-step explanation:

<a = 90° (180-90 supplementary angle)

<b = 90° (180-90 supplementary angle)

<d = 48° (180-132 supplementary angle)

<e = 132° (opposite angle)

<c = 42° (interior angles of a triangle equal 180. 180-48-90=42)

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