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Arc GHF = 360º - ( 180º - 56º ) 

from 1000 to 9999  is   9000 numbers

   stating with 1001  and ending with 9996    there are   9000/7 =~ 1286 numbers  ARE divisible by 7....

          you can finish.....

Alright, Knucklehead 

the diagonal is 2 * height of the equilateral triangles       using side length = L

  height :

      sin 60 = height/L

        L sin 60 = height                   sin 60    is   sqrt 3/2

            2 * height then equals   L sqrt 3   = AD 

then   AD      to      BC  which equals L   becomes      Lsqrt3  / L    = sqrt 3

Sorry, I just changed it. The question was supposed to ask what AD/BC was, not AB/BC.  

If they are equilateral triangles, all of the lines in the figure are of the same length

   then  AB/BC = 1

Here is a picture:

Do you rememebr how to find the minumum point of a quadratic equation? (a parabola)    

           min is at   - b/2a         b = -8.504        a = .04   

a = 11, b = 13, c = 12, d = 9, and e = 11, and their sum is 56.

4-0-0-0

3-1-0-0

2-2-0-0

2-1-1-0

1-1-1-1

We don't need things like 0-0-3-1, 0-0-2-2 etc. because they're identical and would be the same thing.

So there are only 5 cases. 

Hope that helps and please correct me if I'm wrong 

thanks admin!

How do you know what's behind that blurriness?

Suppose that f(x) is a function such that f(xy) + x = xf(y) + f(x) for all real numbers x and y. If f(-1) = 5 then compute f(-1001).

Let  A = number of adult tickets sold and  S = number of student tickets sold.

Number of tickets sold equation:  A + S  =  250

Value of tickets sold equation:  10.50A + 3.75S  =  2071.50.

Solving the first equation for S:  S  =  250 - A.

Substituting this into the second equation:  10.50A + 3.75(250 - A)  =  2071.50

--->                                                             10.50A + 937.50 - 3.75A  =  2071.50

--->                                                                           6.75A + 937.50  =  2071.50

--->                                                                                          6.75A  =  1134.00

--->                                                                                                 A  =  168

Knowing the value of A, you can now find the value of S.

Picture a right triangle with angle(x) being an acute angle;

then, the side opposite to angle(x) = 2ab 

  and the side adjacent to angle(x) = a² - b².

Finding the hypotenuse:  hyp²  =  (a² - b²)² + (2ab)²

                                                  =  [ a⁴ -2a²b² + b⁴ ] + [ 4a²b² ]

                                                  =  a⁴ + 2a²b² + b⁴ 

                                                  =  (a² + b²)² 

--->     hypotenuse  =  a² + b² 

sin(x)  =  opposite / hypotenuse  =  2ab / (a² + b²) 

Woah! Thank you so much! I understand what drawing those lines was meant to do! Thanks!

x/y + y/x  =  -1     --->     xy( x/y + y/x )  =  xy( -1 )

                           --->                x² + y²  =  -xy

                           --->         x² + xy + y²  =  0

Since, when factored:  x³ - y³  =  (x - y)(x² + xy + y²)  and  x² + xy + y²  =  0

--->     x³ - y³  =  (x - y)( 0 )  =  0

This is a right-angled triangle with QR as the hypotenuse.  Let PQ be the Opposite to angle at R, and PR be the Adjacent.

tanR = 4sinR  means 1/cosR = 4, or cosR = 1/4

But cosR = PR/QR = PR/20

So PR/20 = 1/4

Hence PR = 5

Guest #1 has the right idea, but has missed a minus sign. 

\(\frac{c-1}{6-(-3)}=\frac{1-5}{-3-5}\\\frac{c-1}{6+3}=\frac{-4}{-8}\\\frac{c-1}{9}=\frac{1}{2} \\c-1=\frac{9}{2}\\c=\frac{11}{2}\)

If  a  is inversely proportional to  b  then there is some constant  k  such that:  a  =  k / b.

Since  a = -6  when  b = 12     --->     -6  =  k / 12     --->    k  =  -6 · 12  =  -72.

For this problem, the formula is:  a  =  -72 / b.

When  b = -2     --->     a  =  -72 / -2  =  36. 

5x - 5 = 3x + 15  | -3x + 5

     2x = 20          | :2

       x = 10

5*10 - 5 = 50 - 5 = 45

It is supposed to be a integer

I don't see a word integer 

If a side TO is the base, the possibilities are limited   1,2,3.......21

But, if a side TO  is one of 2 legs, the possibilities are practically endless    6,7,8.................∞

( I hope that I understood the question correctly. This time I have more questions than answers...)