Riley is building an ant farm for his school's science fair. He has enough materials to build a farm that is 1000 square inches in total, 9 square inches of which will be taken up for food and water sources. Of the remaining available space, each ant needs at least 1 square inches to themselves. What is the maximum amount of ants Riley's ant farm can house?

991 ants

step by step explanation:

amount of area excluding the area needed for food and resources= 1000-9=991 Square inches

area each ant needs= 1 square inch

number of ants= 991÷1= 991 ants

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.