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maw [93]
3 years ago
6

The area of Mr. Harrison's rectangular vegtable garden can be reresented with the expression 8x + 16. Using the distrubutive Pro

perty, rewrite 8x + 16 as the product of the width (4 meters) and the length. Explain.
                -----------------------------------------
                |                                                |
                |                                                |
 4 meters |                                                |
                |                                                |
                 -----------------------------------------
                                    ?

Mathematics
1 answer:
ra1l [238]3 years ago
7 0
I hope this helps you

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The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
Georgia [21]

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

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3 years ago
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You just do.

Step-by-step explanation:

That's all there is

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3 years ago
What is the vertex of the parabola f(x)=-(x-3)^2+25
zubka84 [21]

Answer:

(3,25) is the vertex

Step-by-step explanation:

f(x)=-(x-3)^2+25

This equation is written in the form

y = a(x-h)^2 +k

Where (h,k) is the vertex of the parabola

(3,25) is the vertex

8 0
3 years ago
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Does anyone know the step by step for this 9(m +5) - 3(m - 2) = 8m + 31
tigry1 [53]
<h3>Answer :</h3>

<u>Given</u> :

  • 9(m + 5) - 3(m - 2) = 8m + 31

We have to find value of m.

➠ 9(m + 5) - 3(m - 2) = 8m + 31

➠ 9m + 45 - 3m + 6 = 8m + 31

➠ 9m - 3m + 45 + 6 = 8m + 31

➠ 6m + 51 = 8m + 31

➠ 51 - 31 = 8m - 6m

➠ 20 = 2m

➠ m = 20/2

➠<u> m = 10</u>

<h3>Hope It Helps!</h3>

6 0
3 years ago
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