Joaquin needs twelve and one-half feet of floor trim to go around the inside of a closet. He has one piece of trim that is three and three-fourths feet and another piece of trim that is three and one-half feet. How many more feet of trim does Joaquin need for the closet?

5 1/4

Step-by-step explanation:

Joaquin needs twelve and one-half feet of floor trim to go around the inside of a closet.

This is written Mathematically as: 12 1/2 feet

He has one piece of trim that is three and three-fourths feet

= 3 3/4 feet

Another piece of trim that is three and one-half feet.

= 3 1/2 feet

How many more feet of trim does Joaquin need for the closet?

This is calculated as the:

Total number of feet of trim he needs - sum of (3 3/4 + 3 1/2)

12 1/2 - [ 3 3/4 + 3 1/2]

12 1/2 - [ 3 + 3 + (3/4 + 1/2)]

12 1/2 - [ 6 + ( 3 + 2/4)]

12 1/2 - [ 6 + 5/4]

12 1/2 - [ 6 + 1 1/4]

12 1/2 - [ 7 1/4]

12 - 7 + ( 1/2 - 1/4)

5 + ( 2 - 1/4)

5 + 1/4

= 5 1/4

Hence, Joaquin need 5 1/4 more feet of trim

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.