A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x3+8x=450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.4 inches 5 inches 9 inches 10 inches

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calculista calculista · Answer 1 · 2018-10-01T03:46:43+02:00

Let

x-------> the length side of the original cube

we have

[tex]2x^{3} +8x=450\\2x^{3}=450-8x[/tex]

Divide by [tex]2[/tex] both sides

[tex]x^{3}=225-4x[/tex]

The system of equations is equal to

[tex]y=x^{3}[/tex] --------> equation [tex]1[/tex]

[tex]y=225-4x[/tex] --------> equation [tex]2[/tex]

using a graphing tool

see the attached figure

we know that

the solution of the system of equations is the intersection both graphs

therefore

the solution is

[tex]x=5.86\ in[/tex]

therefore

the answer is

[tex]5.86\ inches[/tex]

abidemiokin abidemiokin · Answer 2 · 2021-10-25T16:40:57+02:00

The side length of the original cube on factorizing the cubic expression is 5 inches: Option B is correct

Given the equation that represents the given statement expressed as:

[tex]2x^3+8x=450[/tex]

To get the value of x, we will need to factorize the given polynomial as shown:

[tex]2x^3+8x=450[/tex]

Divide both sides by 2

[tex]x^3+4x=225\\x^3+4x-225=0\\x(x^2+4) = 225[/tex]

Using the cubic formula, the value of x is 5inches

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