Arectangular prism measures 2“ x 4“ x 8” what is the side length of a cube with the same volume show work!

4 inches.

Step-by-step explanation:

Start by finding the volume of the rectangular prism.  You can do this by multiplying the length times the width times the height, or 2 times 4 times 8.  This is 64 cubic inches.

Now, you need to find the side length of a cube with a volume of 64 cubic inches.  The formula for the volume of a cube is the side length to the third power (cubed).  Now, you are trying to find s, where .  Another way to write this is .

Now, we just need to find the cubic root of 64, or the number that can be multiplied by itself three times to get 64.  This is fairly simple to find, and you can find that 4 times 4 times 4, or 4 cubed, is equal to 64.  This means that the side length of the cube is 4 inches.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct