geno3141

I'm going to use "crt" to represent the cube root.

Also, I'm going to use this formula:  (a - b)³  =  a³ - 3a²b + 3ab² - b³

y  =  [ x - ( crt(2) + crt(4) ]³

   =  x³ - 3·x²·( crt(2) + crt(4) ) + 3·x·( crt(2) + crt(4) )² - ( crt(2) + crt(4) )³

   =  x³ - 3·crt(2)·x² - 3·crt(4)·x² + 3·crt(4)·x + 12·x + 6·crt(2)·x - 6 - 6·crt(2) - 6·crt(4) 

Let       B =  number of burgers

      B - 2  =  number of fries

           D  =  number of drinks.

B + (B - 2) + D  =  53

  B + B - 2 + D  =  53

            2B + D  =  55

   6·B + 3·(B - 2) + 2·D  =  204.00

         6B + 3B - 6 + 2D  =  204.00

                       9b + 2D  =  210.00

Combining these two equations:

     9B + 2D  =  210                                        --->      9B + 2D  =   210

     2B +   D  =    55     --->   (multiply by -2)   --->     -4B - 2D  =  -110

    (adding down the columns)                                   5B          =  100

                                                                                            B  =  20

Since  2B + D  =  55   --->   2(20) + D  =  55   --->              D  =  15

Since the number of burgers is 20, the number of fries is 18, and the number of drinks is 15.

[ 1 + sqrt(3) ]⁶

=  ₆C₀·(1)⁶·(sqrt(3i))⁰ 

    +  ₆C₁·(1)⁵·(sqrt(3i))¹ 

        +  ₆C₂·(1)⁴·(sqrt(3i))² 

            +  ₆C₃·(1)³·(sqrt(3i))³ 

                +  ₆C₄·(1)²·(sqrt(3i))⁴ 

                    +  ₆C₅·(1)¹·(sqrt(3i))⁵ 

                        +  ₆C₆·(1)⁰·(sqrt(3i))⁶

Since there are 7 letters in "ELLIPSE", the answer will be 7! divided by 2! (because the letter "E" is used twice) and then divided by another 2! (because the letter "L" is used twice).

It has to appear at least twice -- in the 41^st row.

You can check if it appears more often by checking the first 10 (or so) rows to see if it appears in the more central portion of the triangle.

After that row, the numbers in the central portion are too large to give any more 41s.

From the top (12") side to the bottom (9") side is 11" (found by adding the two vertical values (7" and 4") on the left-hand side.

Since there is a 3" segment on the top-right, the bottom-right length is 8" (11" - 3").

The horizontal value at the bottom-left is 8"; the horizontal value at the bottom-right is 9", for a total of 17".

Since the top-left length is 12", the top-right length is 5" (17" - 12").

Now, draw in some line segments and see if you can finish this. 

Good luck!

There are four choices for the bottom scoop, then three choices for the next scoop, then two choices, then only one choice.

There are  4 x 3 x 2 x 1  =  4!  ways.

f( sqrt(x + 1) )  =  1/x

To find f(2), we first need to find the value of x that makes  sqrt( x + 1 )  =  2

Squaring both sides:                                                                       x + 1  =  4

So:                                                                                                        x  =  3

Now, we can replace x with 3:  f( sqrt(3 + 1) )  =  f( sqrt(4) )  =  f(2)  =  1/3

This site is good for answering questions about comma usage:

  https://www.grammarbook.com/punctuation/commas.asp

If you choose A, then you are including the "Oxford comma"; if you choose C, then you aren't.

Either is correct, provided that you are not told otherwise (for instance, newspapers generally don't include the extra comma).