If (5, 4) and (7,2) are the endpoints of a diameter of a circle, what is the equation of the circle?

  (x -6)^2 +(y -3)^2 = 2

Step-by-step explanation:

The midpoint (C) is the center of the circle:

  C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)

A circle with center (h, k) that goes through point (a, b) can be written as ...

  (x -h)^2 +(y -k) ^2 = (a -h)^2 +(b -k)^2

Using the values for this problem, we get ...

  (x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2

  (x -6)^2 +(y -3)^2 = 2

answer: 414,377,008

step-by-step explanation:

just multiply it

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is