Melody

No it is just  a little kid playing make believe.

Thanks for showig us Alan,

I tried to do somthing similar using matrices but got in a big mess.

I didn't think of the obvious things.  :(

Glowlife,  if you are given an answer, maybe from your teacher, then please show us  (with the logic behind it if possible).

I think your answer is too big Max ://

If the beads were just in a circle, where just rotations are the same then the answer woud be 5! = 120

But there are less options than this because of the reflection aspect.

As far as reflection goes, these 3 are the same

So I am thinking tht the answer might be  120/3  =  40

Hi Max, it is great to see you here again !

It is a good start  

Here is how I approached it

\(xyz=720\\ xy+xz+yz=333\\ \sqrt[3]{333}\approx 8.9\)

this means that at least one of the dimensions is 8 or less, and at least one is 9 or more

Factor  720 and you get    

\(720=2^4*3^2*5\)

the factors 8 and smaller are  1,2,3,4,5,6,8   

Try x=8 

If x=8 then  yz=720/8 = 90

8y+8z+90=333   so     8y+8z = 333-90 = 243   

But 243 is not divisable by 8 so 8 is not one ofthe dimensions.

Try x=6     I ran into the same problem

Try x=5      same problem

Try x=4    same problem

Try x=3

If x=3 then  yz= 720/3 = 240

3y+3z+240=333

3y+3z=93  so y+z=31

31=15+16, that sounds promising

If the sides, x,y and z  are  3, 15, and 16  then

(3*15)+(3*16)+(15*16) = 45+48+240 = 333  Bingo

the sides are   3,15 and 16

Does such a polynomial exist?

APR stands for Annual perscentage rate.     

Its simple interest and 6 months so I assume that is  $450 interest per year.

450/6000 *100 %  =   7.5%

Thanks Kakahi,    

I just want to look for myself   

Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

f(m)=3m^2 - 2m + 11

f(2)=12-4+11 = 19    that is the remainder/

19 is prime

19/(m-2) must be a whole number

m-2=19    or m-2=1

m=21     or   m=3

Just like  Kakashi said :)