A flag is 2 feet by 3 feet. I want to enlarge the flag so that the longest side is 15 feet. How long should the shorter side of new flag be to be proportional to the smaller flag?

10 feet

Step-by-step explanation:

Given

Dimension = 2 feet by 3 feet

Required

Determine the length of the short side if the longer side is scaled to 15 feet

Represent the before and after enlargement as a ratio:

Before Enlargement

Ratio = 2 ft : 3ft

After Enlargement

Ratio = x : 15 ft

Where x represents the length of the shorter side

Since they're both proportional, their ratio must be equal.

So, we have:

2 : 3 = x : 15

Convert ratio to fraction

⅔ = x/15

Multiply both sides by 15

15 * ⅔ = 15 * x/15

15 * ⅔ = x

30/3 = x

10 = x

x = 10

Hence, the length of the shorter side must be 10 feet

x+14

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.