Part 5: Use the information provided to write the standard form equation of each circle.

13. x^2 + y^2 - 26y + 165= 0

14. x^2 + y^2 + 2x + 24y + 140 = 0

15. Ends of a diameter: (-1, -16) and (-1, -10)

The answer to your question is below

Step-by-step explanation:

The standard form of the equation

               (x - h)² + (y - k)² = r²

13.-    x² + y² - 26y + 165 = 0

-Group like terms

        (x²          )  + (y² - 26y         ) = -165

-Complete perfect square trinomials

        (x²         ) + (y² - 26y + 13²) = -165 + 13²

-Simplify

        (x² + 0)² + (y - 13)² = -165 + 169

-Result

        x² + (y - 13)² = 4

14.

       x² + y² + 2x + 24y + 140 = 0

-Group like terms

       (x² + 2x     ) + (y² + 24y     ) = -140

-Complete perfect square trinomials

       (x² + 2x + 1²) + (y² + 24y + 12²) = -140 + 1 + 144

-Simplify

       (x + 1)² + (y + 12)² = 5

15.-

A ( -1, -16)

B (-1, -10)

-Calculate the midpoint

Xm = (-1 -1) /2 = -1

Ym = (-16 - 10)/2 = -13

Center = (-1, -13)

-Calculate the radius

dAB =

-Simplify

dAB =

dAB =

-Result

dAB = 6

radius = 6/2 = 3

-Equation

        (x + 1)² + (y + 13)² = 3²      

        (x + 1)² + (y + 13)² = 9

13. x² + (y - 13)² = 4

14. (x + 1)² + (y + 12)² = 5

15. (x + 1)² + (y + 13)² = 9

Step-by-step explanation:

13. x^2 + y^2 - 26y + 165= 0

h = 0/-2 = 0

k = -26/-2 = 13

0² + 13² - 165 = r²

r² = 4

r = 2

(x - 0)² + (y - 13)² = 2²

x² + (y - 13)² = 4

14. x^2 + y^2 + 2x + 24y + 140 = 0

h = 2/-2 = -1

k = 24/-2 = -12

(-1)² + (-12)² - 140 = r²

r² = 5

(x - (-1))² + (y - (-12))² = 5

(x + 1)² + (y + 12)² = 5

15. Ends of a diameter: (-1, -16) and (-1, -10)

Centre: midpoint of the diameter

(h,k) = (-1-1)/2, (-16-10)/2

= (-1,-13)

Diameter lebgrh= 16 - 10 = 6

Radius = 6/2 = 3

(x - (-1))² + (y - (-13))²= 3²

(x + 1)² + (y + 13)² = 9

1/5

step-by-step explanation:

the dice has 6 sides and there is only one 5 in a dice.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .