Aright square prism has a volume of 360 cubic units.
which could be the dimensions, in units, of the prism? select three options.
3 by 3 by 40
4 by 4 by 20
5 by 5 by 14
2.5 by 12 by 12
3.6 by 10 by 10

The answer is 3 by 3 by 40, 3,60*10*10 and 2.5*12*12

Step-by-step explanation:

We need to express the whole volume in prime factors

360=36*10=9*4*10. From the given answer we can see that 3*3*40 is the best choice, there are others...

The second is 36*10, which can also be written as 3,60*10*10

The third one comes from 9*4*10,wich can also be written as 12*12*2.5

First Option  3 by 3 by 40

Fourth Option  2.5 by 12 by 12

Fifth Option     3.6 by 10 by 10

Step-by-step explanation:

The volume of a straight prism is given by the following formula:

Where

w is the width

L is the length

h is the height

In this case we have a  right square prism. This means that

Therefore the volume will be:

The prism will have two sides of equal length and the product of those sides must be equal to 360 cubic units

If we decompose 360 into its prime factors we get:

Rewriting the terms we have

Observe that:            →   First Option

                              →   Fourth Option

                                →   Fifth Option

answer: 100

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.