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3 years ago

the length of a rectangular sing is 5 time its width. if the sign perimeter is 24 inches. what is the sign area ?

Mathematics

1 answer:

kumpel [21]3 years ago

8 0

Answer:

20 in²

Step-by-step explanation:

Assuming that the width of the sign is x, then from the question, we're told that the length is 5 times it's width, so

b = x inches

l = 5x inches

Again, we're told that the perimeter of the sign is 24 inches, and we know already that the perimeter of a rectangle is given as

Perimeter = 2(l + b), substituting this, we have

24 = 2(5x + x)

24 = 10x + 2x

24 = 12x

x = 24 / 12

x = 2 inches.

Since x is the width of the rectangle, and it's 2 inches, we use it to find the length of the sign.

l = 5 * 2

l = 10 inches.

Then, we are asked to find the area of the sign. Area of a rectangle is given as

A = l * b, so if we substitute, we have

Area = 10 * 2

Area = 20 square inches

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Answer:

sum of the polynomials is $9 x^{3} - 4 x^{2} +3x$

Step-by-step explanation:

Given polynomial is (7 x^3– 4 x^2) + (2 x^3 +3 x)

adding x^3 terms, now we get

$(7+2)x^3-4 x^2+3 x$

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3 years ago

A composite figure is shown.

VikaD [51]

The surface area of the pyramid is 60 square feet

The surface area of the square prism is 480 square feet

The surface area of the cube is 180 square feet

The total surface area is 720 square feet

<h3>Area of Composite figures</h3>

From the question, we are to calculate the surface area of each part of the composite figure

For the cube

Surface area of a cube is given by

$S = 6l^{2}$

Where $l$ is the length of a side

But only have 5 surfaces of the cube are part of the composite figure

∴ Surface area of the cubic part of the figure = $5l^{2}$

From the given information,

$l = 6 \ feet$

∴ Surface area of the cubic part of the figure = 5 × 6²

Surface area of the cubic part of the figure= 180 square feet

For the square prism

The surface area of a square prism is given by the formula,

$S = 2l^{2} + 4lh$

Where $l$ is the length of the sides and

$h$ is the height

But the <u>square surfaces</u> are not part of the surface of the figure

∴ Surface area of the square prism in the figure = $2l^{2} + 4lh - 2l^{2}$

Surface area of the square prism in the figure = $4lh$

From the given information,

$l = 6 \ feet$

$h = 20 \ feet$

Thus,

Surface area of the square prism part of the figure = 4×6×20

Surface area of the square prism part of the figure = 480 square feet

For the pyramid

The pyramid is a square pyramid

The surface area of a square pyramid is given by

$S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }$

Where $l$ is the base length

and $h$ is the height of the prism

But the <u>square base</u> is not part of the surface of the figure

∴ Surface area of the pyramid part of the figure = $l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})$

Surface area of the pyramid part of the figure = $2l\sqrt{\frac{l^{2} }{4}+h^{2} }$

From the given information,

$l = 6 \ feet$

$h = 4 \ feet$

∴ Surface area of the pyramid part of the figure = $2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }$

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= $12\sqrt{25}$

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Hence, the surface area of the pyramid is 60 square feet

Thus,

The total surface area = 180 square feet + 480 square feet + 60 square feet

The total surface area = 720 square feet

Hence, the total surface area is 720 square feet

Learn more on Calculating area of composite figures here: brainly.com/question/13175744

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2 years ago

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Yuri [45]

Answer:

[See Below]

Step-by-step explanation:

✦ Turn into decimals:

$\frac{10}{12}=0.83$

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So $\frac{10}{12}$ ≈ $\frac{5}{6},\frac{30}{36},and,\frac{50}{60}$ .

~<em>Hope this helps Mate. If you need anything feel free to message me. </em>

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3 years ago

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Answer:

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3 years ago