ElectricPavlov

(5x^2 +3x^2)   + (-2x + x)  +  ( -4)

8x²  - x - 4

the amount of space to be divided equally    =  3 3/4 - 2 1/2  =  1 1/4 inches

1 1/4  / 2  =   5/8  inch on each side of the label to the edge  

vertex   -2, -3

Vertex form of parabola:    y = a (x-h)² + k

y = a  (x+2 )^2   - 3      Now look at x = -4   the function needs to be = -1

      x^2+4x+4    - 3 = -1

      a(16 -  16 + 4) - 3 = -1

          4a = 2

             a = 1/2

y = 1/2 (x+2)² -3

Ratio of red to yellow    3.5 : 4.5       3.5  out of 8 are red    or   3.5/8

3.5/8  * 12 cups = 5 . 25 cups    or    5 1/4 cups red

6 x 6 x 6 = 216 possible rolls

'5' rolls

113

131

311

221

212

122       6 out of  216      (I think)

Sorry..... I misread (actually didn't read the whole Q)...

23 people must shake hands with AT LEAST 2 other people

23 x 2 = 46 handshakes    ....but each involves TWO people    sooooo   46/2 = 23 handshakes

Formula for distance from a point to a line :

3x+4y-5 = 0   (your line)       point (0, 0 )  means  x₁=0   y₁=0

a = 3   b = 4   c = -5

d=|ax1+by1+c| / sqrt(a2+b2)                    thry this ....let us know what you find !

23 people must shake hands with 22 other people  

   this would be 23 x 22 = 506 handshakes BUT two people are involved with each handshake

     so   506 /2 = 253 handshakes

Correct-o-mundo !

These questions are st up like this:

1/x + 1/y = 1/ t         t = 2 hours

1/5  + 1/y = 1/2        solve for y...the time for y alone