CPhill

y int  =   3(0) - 6y = 18   ⇒     y = -3

x int   =   3x - 6(0) = 18  ⇒     x = 6

We can form a right triangle with legs of 3 and  6

The distance between  the two intercepts  is the hypotenuse = sqrt [6^2 + 3^2]  = sqrt (45)  =3 sqrt (5)

2(x - 8)^2  + 4   =

2 (x^2 - 16x + 64) + 4  =

2x^2 - 32x + 128 + 4  =

2x^2 -32x + 132

a = 2

b = -32

c = 132

So

3ax^2  + 2bx + c  =

6x^2- 64x + 132         

6  [ x^2 - (32/3)x + 22]       complete the square on the terms in the brackets

                                           Note : ([ 32/3] [1/2]) =  (16/3)^2   =256/9

6 [ x^2 - (32/3)x  + 256/9  + 22 - 266/9 ]  =

6 [ (x - (16/3)]^2  +  6 [ -58/9]  =

6 [ x - (16/3) ]^2  -116/3

h  = 16/3

THX for confirming my answer, BuilderBoi  !!!!

Since O  is the circumcenter  of    ABC,  then   AO = BO = CO =  the circumradius

Then angle ABC is an inscribed  angle in the  circumcircle  =  30°

But angle AOC  is  a central angle  intercepting  the same arc  as angle ABC

So  angle AOC  =  2 * angle ABC  =  2 * 30°  =  60°  

y  =3x + 8

So

x^2  + [ 3x +8 -1]^2   = 10

x^2 + [3x + 7]^2   =10

x^2 + 9x^2 + 42x + 49  =10

10x^2 + 42x + 39  = 0

The sum of the two solutions to this   =   -42 /10   = -4.2

The x  midpoint  of  these two solutions =  [sum of two solutions / 2 ] =  (-4.2 / 2 )  =   -2.1

And the y coordinate of this midpoint is  3(-2.1) + 8 =  1.7

(x,y) =  ( -2.1 , 1.7)   

Since EAG   =x

Then EGF  = x   {since  EG is a transversal cutting parallel lines}

But since  EF  = FG  then angle FEG  also  = x 

So

BEF  + FEG  + AEG   =180

130 + x  + x +  x  =  180

130 + 3x  = 180

3x  =  180 - 130

3x  = 50

x = 50 / 3

See here  :

https://web2.0calc.com/questions/pyramids_4

12 ft  =  12 (.3048)  = 3.6576 m

3.6576  =  -4.9t^2 + 42t + 18.9

-4.9t^2 + 42t + 15.2424  = 0

Using the quadratic formula, the ball reaches 12 ft  at

-42 -  sqrt ( 42^2 - 4 (-4.9)(15.2424) )                -42  - sqrt (2062.75104)

__________________________  =              ___________________   ≈   8.92 sec

                 2 * -4.9                                                          -9.8

Very nice, qjin  !!!

We can write   these two equations

2x - 9y   = 14     (1)

8x - 42  = y        (2)

Sub (2)  into (1)

2x - 9(8x - 42)  = 14

2x - 72x + 378  = 14

-70x  = 14 - 378

-70x = -364

x = -364 / -70  =  26/5 =  5.2

y = 8 (5.2) -42  =  -0.4

xy  =  (5.2) (-0.4)   =  -2.08