Apainter places an 11-ft ladder against a house. the base of the ladder is 3 ft from the house. how high on the house does the ladder reach?

The ladder reach 10.58 feet

Step-by-step explanation:

In this problem a rectangle triangle is formed, with hypotenuse = 11 feet, a side = 3 feet and the other side is the unknown, i. e., how high on the house the ladder reach.  

From Pythagorean theorem:

hypotenuse^2 = side^2 + side^2

11^2 = 3^2 + side^2

side^2 = 11^2 - 3^2

side = sqrt(112)

side = 10.58 feet

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.