CPhill

Tanzi uses    1200 ml      when  Maeve uses  (1/3) 1200 ml =   400 ml

Therefore.....she uses  3 times as much in a specified amout of time

So

Maeve should  pour   (3/4) (400 ml)  =   300 ml  into  Tanzi's bottle

Tanzi will have 300 ml  and Maeve will have 100 ml    and.....3 times what Maeve uses = whatTanzi uses in the  same amount of time

We have this relationship :

AX^2  + CX^2  =  BX^2 + DX^2

11^2  + 10^2   = 11^2  + DX^2

100  = DX^2

10   = DX

3a + b + c =    -3       (1)

a + 3b + c =    9        (2)

a +   b  + 3c  =  -6     (3)        add all three equations

4a + 4b + 4c =   0

a + b +c =   0

a + b =  -c                sub this into  (3)

-c + 3c  = -6

2c =  -6

 c  = - 3

Also   a + c  = -b      sub this into (2)

-b + 3b =  9

2b = 9

b =  9/2

And   a + b + c  =0

a + 9/2  - 3  = 0

a + 3/2  =0

a =  -3/2

abc   =  (-3/2)(9/2) (-3)  =   81 / 4

Expected value  = 

Value of win * probability of winning +   Cost of losing * probability of losing =   

2 ( 1/2)  +  -2(1/2)  =  

0

We have a  low over high situation  in terms of  polynomials.....when this happens  there is a horizontal asymptote at y  = 0

So.....0  is not in the  range  of the  function

x(3x - 7)  = -3 + 2x

3x^2  - 7x  = -3 + 2x           rearrange as

3x^2 - 9x  =  -3             divide through by 3

x^2  - 3x  =  - 1        complete the square on x

x^2  -3x  + 9/4 =  -1  + 9/4

(x - 3/2)^2  =  5/4       take  both roots

x - 3/2  =     ± √5/2

x =   3/2   ± √5/2

m= 3    n  = 5     p  =  2

m + n +  p  =   10

-16t^2  -60t  + 54 = 20

-16t^2 -60t + 34  = 0

16t^2  + 60t  - 34  =  0

              -60   +  sqrt [ 60^2  - 4 (16) (-34) ]               -60 + sqrt [ 5776]       

t  =       _____________________________   =     ________________ =

                              2 * 16                                                   32

-60 + 76

_______  =   16 / 32  =     .5 sec

      32

Defined when  x  = 1    →  sin 2  ≈  .909

Undefined when x  = 2   → sin 4  = -.757

Vertex form

y = a ( x  - h)^2  +  k      where  (h,k)  is the vertex  and (x,y) a point on the graph....so....

7 =  a ( 5 -4)^2 + 0

7  = a * 1^2

7 = 1a

a  = 7

150 * 9.9 =    1485 lbs

1485  x 12.50  =  18562.5 miles of yarn

1760  yds in one  mile....so....

18562.5 * 1760  =    32670000 yds

32760000 /  175    =  186685.7 skeins   ≈   187000 skeins  (to the nearest 1000 )