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docker41 [41]
3 years ago
15

A room in the shape of a rectangular prism measures 15 feet by x feet by 12 feet. Write a simplified expression for the volume (

in cubic feet) of the room.
Volume = ft3
Mathematics
2 answers:
34kurt3 years ago
6 0

Answer: Volume =180x\ ft^3

Step-by-step explanation:

We know that the volume of a rectangular prism is given by :-

V=length\times width \times height

Given : A room in the shape of a rectangular prism measures 15 feet by x feet by 12 feet.

Then, the volume of a rectangular prism will be :-

V=15\times x\times12\\\\\Rightarrow\ V=15\times12\times x\\\\\Rightarrow\ V= 180x

Hence, the simplified expression for the volume (in cubic feet) of the room will be : 180x\ ft^3

zloy xaker [14]3 years ago
5 0
180x feet^3

this is the answer because volume is lwh so 15 x 12 x x is 180x the labeled is 180x ft.^3
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Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.
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Answer:

x^2(3x-2) cubic inches OR in^3

OR

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS

<em>-</em>

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Volume = v, abc = 3 sides of cube (height, width, length)

Using the formula for volume in a cube,

v = abc

We can solve this.

If one side is (3x-2)in,

  • (3x-2)(x)(x) = v.... x are the other two sides
  • x^2(3x-2) = v

x^2(3x-2) cubic inches OR in^3

If all sides are (3x-2)in,

Use the formula,

(a - b) ^{3}  =  {a}^{3}  + 3ab(b - a) -  {b}^{3}

We can solve this.

  • (3x-2)(3x-2)(3x-2) = v
  • (3x-2)^3 = v.... 3x = a and -2 = b
  • (3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v
  • 27x^3 + 18x(2-3x) -8 = v
  • (27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 8
  • 3x(9x^2 -18x +12) = v... Take 3 as common again in the brackets
  • 3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets
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  • 3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v

3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3

___

If you have any questions regarding formulas or anything, comment and I will get back to you asap.

___

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