Write the equation in standard form and then find the center (h, k) and
x^2+8x+ y2 + 4y - 5= 0

Center is at (-4, -2) and the radius = 5.

Step-by-step explanation:

Convert to Standard form:

x^2 + 8x + y2 + 4y - 5= 0  

Completing the square:

(x + 4)^2 - 16 + (y + 2)^2 - 4 = 5

(x + 4)^2 + (y + 2)^2  = 5 + 16 + 4

(x + 4)^2 + (y + 2)^2  = 25

(x - h)^2 + (y - k)^2 = r^2     Comparing:-

The center is at (-4, -2) and the radius = 5.

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.