ElectricPavlov

There are 5! possible 'words'n  (120)

AFTER usamo   is usaom   usmao   usmoa   usoam  usoma

                115         116       117         118        119      120

Six choices    246   264  426   462  624  642

The RED ones are divisible by 8    .... I think you can take it from here !  

If x and y are POSITIVE integers and they are not EQUAL, then

30(1) + 18(2) = 66

I think Geno's answer below is best !  (as Q did not specify x and y are positive as I answered)

The sum of the interior angles of a polygon is given by the formula:

sum = 180(n-2) degrees

2014 >= 180(n-2)

11.18 >= n-2

13.18 >= n    

n <= 13.18       So 13 sides is correct !  

First, expand the terms

4x^2-8x+8      - 7x^3 + 21x - 7       now collect 'like' terms

-7x^3   +4x^2    - 8x+21x    + 8 - 7       simplify

-7x^3  + 4x^2   + 13x   +` 1              

       now you can see the coeffiicients   ( -7   4    13     and 1  (the constant coefficient) ) ....square them and add them together....

JUan has HOW MANY cheesecakes?

If you put the line equations in the form  y = mx + b   the slope is m

First one  y -ax =2

                y = ax + 2        the slope of this line is 'a'

                                       perpindicular slope will be  - 1/a

Line 2  x + 23y = 138

                 23y = -x + 138    divide both sides by 23

                     y = -1/23  x  + 6       slope is -1/23     

                         for these lines to be perpindicular:    - 1/a  = -1/23        so a = 23

Here is a graph:

https://www.desmos.com/calculator/fqvxr43leu

Here is a graph if you are stuck.....

https://www.desmos.com/calculator/94brhqodjk

vertex is directly between the focus (2,6) and directrix x=0

   so   vertex is  1,6

this parabola opens to the right.....     can that get you started?

     a  is a multiple of 3     say 9

     b is a multiple of 6     say 12        a - b  = -3    is NOT a multiple of 6    is NOT a multiple of 2

                                                             b IS a multiple of 3     and a-b IS a multiple of 3

A, B