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BaLLatris [955]
2 years ago
15

be rectangular prism and rectangular pyramid have the same volume. determine the value of x, the height of the pyramid.

Mathematics
1 answer:
Marina CMI [18]2 years ago
7 0
ANSWER

x= 9 \: in

EXPLANATION

The volume of a rectangular prism is given by the formula,

V = l \times b \times h
We substitute the dimensions to obtain,

V = 6 \times 3 \times 12 \: {in}^{3}

The volume of the rectangular pyramid is,

V = \frac{1}{3} \times 6 \times 12 \times x \: {in}^{3}

Equating the two volumes gives,

\frac{1}{3} \times 6 \times 12 \times x = 6 \times 3 \times 12

We divide through by 6×12 to get,

\frac{x}{3}=3

We solve for x to obtain,

x = 3 \times 3

x = 9 \: in
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4. The students in Mr. Michael’s art class are decorating a booth for Harvest Day. They have blue cloth that is 60 inches long,
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Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.

<u>a.</u>  

As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find <u>GCF(greatest common factor) of 60, 48 and 72. </u>

First we will factor out all three numbers completely......

60=2*2*3*5\\ \\ 48=2*2*2*2*3\\ \\ 72=2*2*2*3*3

The common factors are: 2, 2 and 3

Thus the GCF = 2*2*3=12

So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.

<u>b. </u>  

For finding the number of pieces for each color cloth, we will just <u>divide the length of each cloth by 12</u>. So...

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Number of pieces for gold cloth =\frac{48}{12}=4 and

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4 0
2 years ago
Solve the equation 6/5y-10=-4<br> X=
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6/5y-10=-4

move -10 to the other side

sign changes from -10 to 10

6/5y-10+10= -4+10

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Mutiply by 5/6 for both sides

6/5(5/6)y=6(5/6)

Cross out 6/5 and 5/6 , divide by 5 and 6 then becomes y

Cross out 5 and 6 on the right side

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Answer : x= 5

3 0
3 years ago
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