CPhill

We have 10 balls

P ( green  then  blue )  =   3 /10  * 2 / 10   =    6 / 100  =  3  / 50

The center  is  ( -9, -6)

We jhave 2 possible outcomes trhat do not show a "1"  on the first spinner

And there is only  1 outcome where the second spinner shows a "4"

So......  the number or outcomes  is  2 * 1   =  2

We have three possible outcomes  on every spin

So...on three spins, we have

3 spins  * 3 outcomes per spin  =  27  different outcomes  

y  = 18x^2 + 4x  + 20

y = 18  (x^2  + 4/18x   +  20/18)   complete the square on x

y  = 18  ( x^2 + 4/18x + 16/1296 + 20 / 18  - 16/1296 )

y  = 18 [ ( x + 4/36)^2 +  89/81]

y = 18(x + 4/36)^2  + 178/9

(y - 178/9 )  = 18 ( x + 4/36)^2

(1/18) (y - 178/9)  = (x + 1/9)^2

The vertex  is  ( -1/9, 178/9 )

This parabola opens upward

We  have that     4p  = 1/18    ⇒ p   = 1/72

So....the focus is  at    ( -1/9, 178/9 + 1/72)  = (-1/9, 475/24 )

The ladder length will form the hypotenuse of a right triangle and the 11.8 ft will form the opposite leg to the angle we are seeking....to find this angle, use the sine inverse....so we have

arcsin (11.8 / 12)  ≈  79.5°

So..it is unsafe

Here's a pic :

x^2  + y^2  + 4x  + 2y  - 4   = 0

x^2 + 4x + 4  + y^2 + 2y  + 1  =  4 + 4 + 1

(x + 2)^2  +  (y + 1)^2   =  9

The center is  ( -2, -1)  and the radius is 3

EDIT TO CORRECT ASLIGHT ERROR  !!!

We need to  complete the square on x and y for each one of these.....you should review how to do this if you are unsure of the procedure....I'll do the first one in some depth

1) x^2 + y^2 + 24x + 10y + 160 = 0

x^2 + 24x +  y^2 + 10y  = -160

Take 1/2 of 24, square it = 12^2  = 144...add to both sides

Take 1/2  of 10, square it  = 5^2  = 25....add to both sides

x^2 + 24x + 144  + y^2 + 10y + 25  = -160 + 144 + 25  factor and simplify

(x + 12)^2  + ( y + 5)^2  = 9

The center is  ( -12, -5)  and the radius  = 3

2) x^2 + y^2 - 6x + 10y = 97

x^2 - 6x + 9  + y^2 + 10y  + 25  =  97  + 9 + 25

(x - 3)^2  + ( y + 5)^2  = 131

The center is  ( 3, -5)  and the radius  is √131

3) x^2 + y^2 +26x + 28y = -364

x^2 + 26x + 169  + y^2 + 28y + 196  = -364 + 169  + 196

(x + 13)^2  + ( y + 14)^2  =  1

The center is  (-13, -14)  and the radius  is 1

If the difference in the largest and smallest angle is 44 degrees.....then  the common difference between each successive angle measure is 11°

And the sum of the angle measures  is 540°

Let n   be the smallest angle....so we have

n +  (n + 11) + (n + 22)  + (n + 33)  + (n + 44)   = 540     simplify

5n  + 110  =   540       subtract  110  from both sides

5n  = 430      divide both sides by 5

n  = 86° =   the smallest angle

27.  9y^2 - 16x^2   = 144

Divide through by 144 to get to this form

y^2   -  x^2     = 1

___     ____

16         9

The center  is  (0, 0)

The  foci  are given  by

(0, ±√ [ 4^2 + 3^2 ] =

(0, ±√25 )  =

(0, ±5)

28.  The correct equation is

y^2    -  x^2    

___      ___  =    1

144       25