Select the correct answer. A swimming club can currently accommodate up to 100 members for a year-long training program. They plan to increase their pool capacity to accommodate up to an additional 75 members into the program every year. To make a profit, the club must have at least 50 members enrolled in the program. The club manager expects the minimum membership requirement for making a profit to increase by 20% every year.

The manager modeled this situation with a system of inequalities, where x is time from today, in years, and y is the number of members. She graphed the system to show the solution region when the club is making a profit.
What system of inequalities did the manager create?

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough

the answer to that one is b