A cube has an edge length of 4 inches. You halve each side length. How many times smaller is the volume of the new cube?

8 times smaller

Step-by-step explanation:

The original volume is: V = x^3 , where x is the edge length. So: V = 4^3 = 64 inches cubed.

If we halve each side length, 4 becomes 2, so our new volume is: V = 2^3 = 8 inches cubed.

To find how many times smaller, we take the original volume and divide by the new volume: 64/8 = 8

Thus, the new cube is 8 times smaller.

Hope this helps!

8 times smaller

Step-by-step explanation:

Cube with s = 4 in:

Volume = 4³ = 64in³

Cube with ½(4) = 2 in

Volume = 2³ = 8 in³

8/64 = 1/8

one that is bigger than 3 1/2

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!