CPhill

The form is  (x - h)^2 + (y - k)^2 = r^2

Using the first two points and the square of the distance formula to equate the radius's we have

(-1-h)^2  + ( 2 - k)^2 =    (3-h)^2 + (2 - k)^2

h^2 + 2h + 1  =  h^2 - 6h + 9

8h  =  8

h =  1   this is the x coordinate of the center

Using the last two points and doing the  same thing we have

(3 - 1)^2 + (2 - k)^2  = (9 - 1)^2  + (0 - k)^2

4 + k^2 -4k + 4  =  64  + k^2

-4k + 8 =  64

-4k  = 56

k= -14

h +  k =    1  - 14  =     -13

4z^2 + cz +  0  ???

We can't get a squared binomial out of this Blizzardshine....you sure you wrote it correcty  ??

Rewrite as

10r^2 + 68r  =  45       divide  through by 10

r^2  + (68/10)r  = 45/10

r^2 + 6.8r   =  4.5         take 1/2  of  6.8 = 3.4  square it = 11.56  add to both sides

{ the number in  red is what we need later }

r^2 + 6.8r + 11.56  =  4.5 + 11.56

(r + 3.4)^2 =  16.06      take both roots

r + 3.4 =   ±√ 16.06

r = √16.06  - 3.4  ≈  .6075 

or

r = - √16.06 - 3.4  ≈ -7.4075

Let the total number  of people  =  N

(1/3)N are adults

(2/3)N are boys and girls

Of this  (5/12)(2/3)N are boys =  (10/36)N  = (5/18)N     

A nd (7/12)(2/3)N are girls =   (14/36) N =  (7/18)N

Note (1/3)N  =(6/18) N

No. boys * no. of keychains rec'd  + No. adults * keychains rec'd =  368

So

(5/18)N* 2 +  (6/18) N * 6 =  368

(10/18)N  + (36/18)N =  368

46N / 18  =  368

23N / 9 = 368

(368 * 9 )  / 23 =  N =   144

No. of chldren = (2/3) 144 =  96

No. of adults =  48

96 - 48 =    

48 more 

We have the form

x =  a ( y - k)^2 + h          where the vertex is  (h , k)

Since the point   (2,0)  is on the  graph

2  =  a ( 0 -  -1)^2  + 4

2 - 4  = a *1

-2 = a

So

x =  -2 ( y + 1)^2  + 4

x =  -2 ( y^2 + 2y + 1) + 4

x = -2y^2 - 4y - 2 + 4

x = -2y^2 - 4y + 2

x = ay^2 + by + c

a = -2   b = -4     c = 2

a + b + c  =   

-4

60  - 18.5 = 

41.5  in

The points (1,1) and (0,4)  are on the graph

The slope is    ( 4 - 1)  /( 0 -1) =  3/-1  =   -3

We either have

y ≤  -3x + 4    

or

 y ≥ -3x  + 4

(0,0)  makes   the first true......but this point is  not in the feasible region

So

y  ≥ -3x + 4 is true  

So

3x + y  ≥  4

2 + 1/2 yds =   (5/2) (3ft) =  15/2 = 7.5 ft

5 + 1/3 yds  =  ( 16/3) (3 ft) = 16 ft

Amount needed  =

( 7.5 * 16 ) sq ft   * (1/2) oz  = 

60 oz

Here's my approach to this one

We only need to  consider the group of three.......the other group of 4 will meet our requirement automatically

Case 1  - 2 men and 1 woman in the group of 3

We have the choice of  (3 men x 2 men x 4 women) =  24 groups

Case 2  - 1 man  and  2 women in the group of 3

We have the choice of  (3 men x 4 women x 3 women ) =  36 groups 

So

24 +  36 =    60 ways

If  the circle is tangent to the y axis at (0,2)  the center must be (c , 2)  where c is the radius

Using the squares of the  distance formula

(c- 0)^2  +  ( 2 - 2)^2  = (12 - c)^2 + (2 - 0)^2

c^2 =  c^2 - 24c  + 144 + 4

24c =  148

c = 148/24 =  37/6  =  the radius