To make a punch Anna adds 8 ounces of apple juice for every 4 ounces of orange juice if she uses 32 ounces of apple juice which proportion can she use to find the number of ounces of orange juice x she should add to make the punch

Step-by-step explanation:

If our ratio is apple juice to orange juice, then the proportion will be

If we are looking for how much orange juice she needs if she uses 32 ounces of apple juice, then 32 goes on top of a new ratio and x goes on bottom:

That's the proportion.  If you need to solve it, cross multiply to get

8x = 128 so

x = 16 ounces of orange juice

well what did you do it matters what you did : )

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.