Why are length x width x height and base x height both correct ways to find volume of a rectangular prism?

Answer

Because the base is equal to the area, (L*W). So essentially, they are the same equation!

Explanation:

We normally find the area when dealing with two-dimensional shapes, correct? So, when the shape becomes 3-dimensional, it now includes a base and a height! You multiply these together to get the volume (the amount of space it takes up).

If we were to add a height to a regular rectangle, what was once the entire shape, now becomes the base of a rectangular prism! The length and the width of that prism is equal to the base, which makes both equations equal to each other!

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

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