Just a counting prob
Number of committees =
C ( 7,2) * C(7 ,3) * C ( 9, 4) * C(7 , 5) =
1,944,810 (that's quite a few !!!! )
If x is "very negative," the second trem will go to 0 and the range max will be almost 3
If x is "very postive," the function will approach -inf
So the range is (-inf, 3)
Write the second equation as y = 17 - 7x
Sub this into the first equation
9x - 4 ( 17 - 7x) = 30
9x - 68 + 28x = 30
37x = 30 + 68
37 x = 98
x = 98 / 37
And y = 17 - 7 (98/37) = -57 / 37
(x , y) = ( 98 / 37 , -57 / 37 )
(-4,0) is a root ....so.....
If we shifted this parabola to the right by 4 units the vertex is (0,0) and we would get rid of the bx and c terms
And now..... ( 1 + 4, -7) becomes (5 , -7)
So
y= ax^2
-7 = a (5)^2
-7 = 25a
a = -7 / 25
y= -2x^2+8x-15+3x^2-6x+22 rearrange as
y = x^2 + 2x + 7
The x coordinate of the vertex = -2 / [ 2 * (1) ] = -1
The y coordinate is (-1)^2 + 2(-1) + 7 = 6
xy = 20 ⇒ y = 20/x
xz = 35 ⇒ z = 35 /x
yz = 14
(20/x) (35/x) = 14
700 = 14 x^2
700 / 14 = x^2
x^2 = 50
x= 5sqrt (2)
y = 20 / [ 5sqrt 2] = 4 / sqrt 2
z= 35 / [ 5sqrt 2] = 7 /sqrt 2
xyz = 5sqrt 2 * 4 /sqrt 2 * 7/ sqrt 2 = 140 / sqrt 2 = 70sqrt 2
P(Jack) = 4/ 52 = 1/13
P(Heart) = 13/52 = 4/13
P ( heart and then jack with replacement) = 1/13 * 4 /13 = 4 / 169
(x + 7) (x - 11) = 0
x^2 - 4x - 77 = 0
5x^2 -11x + 4 = 0
Note that 1/a + 1/b = (a + b) / (ab)
The sum of the roots = 11/5 = a + b
The product of the rooots = ab = 4/5
1/a + 1/b = 11/5 / 4/5 = 11 / 4
B
4
7 M
3 4
A C
Triangle ABM would have sides of AB = 7 AM = 3 and BM = 4
But, by the triangle inequality, this is impossible......so what you have described is impossible
