John has a collectible card that is worth three times as much as the value of Kelly's card. Lia has a card that is worth five times as much as the value of Kelly's card. The value of the three cards together is $477. What is the value of Kelly's card?

  $53

Step-by-step explanation:

The ratios of value are ...

  J : K = 3 : 1

  L : K = 5 : 1

So, the ratios together are ...

  K : J : L = 1 : 3 : 5

There are a total of 1+3+5 = 9 ratio units corresponding to a total value of $477. Then each must be worth ...

  $477/9 = $53

Kelly's card is worth 1 ratio unit, so is worth $53.

answer: the answer is ann

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.