Find the standard form for the equation of a circle ( x − h ) 2 + ( y − k ) 2 = r 2 with a diameter that has endpoints ( − 7 , 4 ) and ( 5 , − 5 ) .

(X+1)^2 + (y+1/2)^2 = 225/4

Step-by-step explanation:

Center= (-7+5) /2 = - 2/2 = -1 and (4-5)/2 = - 1/2

Coordinates of the center = (-1, - 1/2 )

(-1 is the h coordinate in the circle equation and -1/2 is the k)

Distance of the diameter= sqrt [(-7- 5)^2 + (4 - - 5)^2]

d = sqrt [(-12)^2 + (9)^2

d = sqrt (144+81)

d = sqrt 225

( the value of the radius in the equation is squared so the radius is (sqrt 225/2)^2=

Radius= 225/4

The equation of circle is: (x - - 1)^2 + (y - - 1/2) = 225/4

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.