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Oh wow , super simple! Thanks for helping me

thank you 

Nice !  I forgot about the other THREE !

The  inverse just reverses the coordinates

So....the  domain and range  of  a function and its inverse switch

The coordinates  ( 2, -3) , ( 5, 0)  and  ( -2, 3)  are on the inverse

Actually....we have four possibilities......

The center  of the first circle  is   (3, 1)

Its equation is (x - 3)^2 + (y - 1)^2  =4

Another possibility is a circle with a center of ( 3, 5)

Its equation is  ( x - 3)^2 + ( y - 5)^2  = 4

Two other possibilites  

A circle with a center of (-1, 1)

Equation is  ( x + 1)^2 + ( y - 1)^2  = 4

A circle with a center (-1,5)

Equation is ( x + 1)^2 + ( y - 5)^2  = 4

See the graph here : https://www.desmos.com/calculator/lgpofoe62f

The radius is 2   so we know the center will be   2   from x = 1      h = 3

                        and the center will be 2 away frm y = 3                 k=1

h,k = 3,1   r^2 = 4

(x-3)^2 + (y-1)^2 = 4 

I'm assuming 9 rolls of a die and the outcome of EXACTLY 2 sixes:

9C2 * 5^7 =2,812, 500 / 6^9 =~27.91%

Using the Law of Sines

sin 36 / 9  =  sin ACB / 7.7

sin ACB = 7.7 sin 36 / 9

arcsin (7.7 sin 36 / 9)  = ACB  ≈  30.19°

So angle  CBA = 180 - 36 - 30.19  ≈  113.81°

So....by the Law of sines

AC/ sin 113.81 = AB/ sin 30.19

AC / sin 113.81  =  7.7 / sin 30,19

AC = 7.7 sin13.81 / sin 30.19   ≈  14.0089

And because the apex angle is bisected

AC / AD  = BC / DB

AC / BC  =  AD/ DB

14.0089 / 9  = AD / DB

( 14.0089 / 9) DB = AD

(14.0089 / 9) DB + DB  = 7.7

(1 + 14.0089/9) DB = 7.7

DB =  7.7 / ( 1 + 14.0089/9) ≈   3.011

So

AD  = 7.7 - 3.011  ≈ 4.689

(2/3) x  = 1

x =  1 /(2/3)

x = 3/2

So...there are (3/2) two-thirds in one

Proof

(2/3) (3/2)   = 1

THX, Alan....I'm gonna' need to ponder this one....!!!!

Triangle ABC:
Using Law of Cosines:
Sides: AB = 7.7 BC = 9 AC = 14.009
Angle ∠ A = 30.191° = 30°11'27″ = 0.527 rad
Angle ∠ B =  36° = 0.628 rad
Angle ∠ C = 113.809° = 113°48'33″ = 1.986 rad

Triangle ADC:
Using Law of Sines:
Sides: AD = 4.688 DC= 10.581 AC= 14.009
Angle ∠ C = 15.096° = 15°5'46″ = 0.263 rad
Angle ∠ A = 36° = 0.628 rad
Angle ∠ D = 128.904° = 128°54'14″ = 2.25 rad

Thank you,

well how advanced do you want your answer to be

They have been added

The answer I have is three half’s 

Thanks 

a/b = 4  multiply both sides by b

a = 4b   divide both sides by a

1 = 4 b/a  divide both sides by 4

1/4 = b/a

Further thought has produced the following:

I guess WolframAlpha used something like this reasoning!

Hmm!  My simplification when |4y-2| is positive leads to incorrect solutions.  i.e. when the solutions are plugged back into the LHS of the original equation the resut isn't zero.   The Wolfram Alpha solutions, on the other hand, do give zero, so they are obviously correct.  I will need to think further about how to obtain these!

Corrected...

Im sorry cphil but 2nd answer is incorrect

7744   works

You got it   !!!!!