Arectangular solid is dilated by a factor of 0.5. how many times larger is the volume of the resulting solid than the volume of the original solid?

The volume of the resulting solid is eight times smaller than the volume of the original solid

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x------> the volume of the resulting solid

y-----> the volume of the original solid

so

In this problem we have

substitute

The volume of of the original solid is eight times larger than the volume of the resulting solid

or

The volume of the resulting solid is eight times smaller than the volume of the original solid

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

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step-by-step explanation: