Find the center and the radius of the circle with the equation:
x^2 + 6x + y^2 + 4y + 12 = 0
a.

center: (3, 2)
radius: 1

c.

center: (6, 4)
radius: 12
b.

center: (-3, -2)
radius: 1

d.

center: (-6, -4)
radius: 12

Center is (-3, -2) and radius is 1

Step-by-step explanation:

By comparing the 2 equations,

⇒ 2gx = 6x

⇒ 2g = 6

∴ g = 6/2 = 3

⇒ 2fy = 4y

⇒ 2f = 4

∴ f = 4/2 = 2

⇒ c = 12

Center = (-g, -f) = (-3, -2)

Radius = √g² + f² - c

           = √3² + 2² - 12 = √9 + 4 - 12

           = 1

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!