CPhill

The remaining vertex  is    (5, -2)

The  circle is  centered at   (5, -2)  and  has a radius of 1

The area will  be 1/4  the area of the circle  =   pi  * 1^2 /  4 =     pi/ 4

For a point - call it X -  inside a rectangle  ( call it PQRS).....the following relationship holds

PX^2 +  RX^2 = QX^2 + SX^2

2^2   +  5^2   + 10^2 + SX^2 

But what you describe is  impossible because   SX^2 =  2^2 + 5^2  -10^2  =  -71

But SX is a positive distance......so squaring  it can only produce a poisitve outcome

Rearrange as

x^2 - 4x + y^2 - 4y =  16          complete the square on x.y

x^2 - 4x + 4  + y^2 - 4y + 4 =  16 + 4 + 4

(x - 2)^2  + ( y - 2)^2 =   24

This is a circle centered at   (2, 2)  with a radius of sqrt (24)  =  2sqrt (6)

The greatest value for  x =   

2  + 2sqrt (6)  = 

 2 ( 1 + sqrt (6) )

Cross- multiplying we get

2x ( x + 4) =  (x + 5)(x -5)

2x^2 + 8x = x^2 - 25      rearrange as

x^2 + 8x + 25  = 0

          -  8 ±√  [8^2 - 4*1*25 ]                          - 8 ±√ [ -36 ]           -   8 ± 6i

x =   _____________________  =              ____________  =   _______  =  - 4 ± 3i

                            2  * 1                                         2                           2

This isn't possible

f(3)  = 0   and f(3) = 28  means this  graph doesn't pass the vertical line test......but all polynomials pass the vertical line test

x^2 + ax   = -14

x^2  + ax + 14  = 0

(x + 14) ( x + 1)   =  0

x^2 + 15x  + 14  = 0

The equation of the first line is    y =  8

The equation of the second line is  x =  4

The intersection of these lines is   ( 4 , 8)

Top   8 x 2 rectangle =   16 cm^2

Middle       5 x ( 9 + 8) rectangle   =  5  x 17 =   85 cm^2

Bottom   right triangle with a height of 5  and a  base of ( 17 - 6 - 3)  =  8

Area =  (1/) 8 * 5 =  20 cm^2

Total area = 

16 + 85 + 20  = 

121 cm^2

Top - half circle with a radius of  (6 -2 -1) / 2 =  3/2  =1.5

Area =  3.14 (1.5)^2

Middle  - a rectangle  with dimensions of  (6 + 1) x  4 =  7 x 4 =  28

Bottom - a rectangle with dimensions  of   6 x 3  = 18

Total area  =

 [ 3.14 * 1.5^2   + 28 + 18 ]  km^2  =

53.065  km^2

Top left - We have a half circle with a radius of ( 8 - 4 + 2)  / 2 = 6/2 = 3     area =     3.14 * 2^2 =  12.56   km^2

Center - We have  an 8  x 2 rectangle  =  16   km^2

And, at the bottom  we have a   5 x 8  rectangle = 40  km^2

Total area = 

12.56 + 16 + 40 = 

68 .56    km^2