How many 1-in. cubes can fit into a 2 by 4 by 2 in.
prism?

16

Step-by-step explanation:

The dimensions of the base of the prism are 4" by 2"; the height is 2".

Looking at the base, we see that (4)(2), or (8) 1" cubes would cover it exactly and wholly.  We'd have a 3-dimensional prism with one layer of 1" cubes.

Now if we add a second layer right on top of the first layer, we'd have used (16) 1" cubes.

To find out how many 1 inch cubes can fit into a prism, we need to find the volume of both the prism and cube.

Cube:

V = 1 x 1 x 1

V = 1 in^3

Prism:

V = 2 x 2 x 4

V = 16 in^3

Then, we'll divide the volume of the prism by the volume of a single cube to figure out how many cubes can fit inside the prism.

16 / 1 = 16

16 1-inch cubes can fit into a 2 by 4 by 2 prism.

Hope this helps!! :)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

its adding 5.5 each time

step-by-step explanation: