Can someone help on these math problems?

1. When the Justices of the Supreme Court assemble each day, each justice shakes hands with each of the other justices. There are a total of 36 handshakes made by the justices. The total number of handshakes, h, for n people is given by the equation h=n2-n/2





2. Find the value of ';c'; that will make 25x2-40x+';c'; a perfect square trinomial





Can someone please explain to me how to do these?


When there is a letter and a 2 the two is supposed to be a square.


ex. x2Can someone help on these math problems?
Last question first.... I do believe that you mean an exponent.





as in x2 means x^2. The number is generally written in a smaller font and superscripted on the base.





Now,


h = (n^2 - n)/2 as I believe that the entire n^2 - n is in the numerator of the fraction.


36 = (n^2 - n)/2


I hate fractions, so multiply by 2


72 = n^2 - n


Get equal to zerio


n^2 - n - 72 = 0


Factor


(n - 9)(n + 8) = 0


Set each factor equal to zero and solve them


n - 9 = 0, n + 8 = 0


n = 9 , n = - 8


Since you can't have negative eight people, the answer is 9 justices.





2. 25x^2 - 40 x + c





(5x - ____) (5x - ____)





Since (using FOIL) you know that making a perfect square trinomial will require that both factors be identical, and since the first terms is 25x^2, you know that you have to have a 5x as the First terms in the factors. You also know that both factors have a negative sign between the terms b/c you have to have a -40 when you combine the outer terms and the inner terms. Since those will both be the same, we basically want HALF of -40x (which is -20x ) to be the product of the Outer terms and the Inner terms. To get that, we need to put a 4 on both of those spaces I have above...


( 5x - 4 )( 5x - 4 )


Now multiply the binomials and you will get 25x^2 - 40x + 16. So, c has to equal 16.