Pythagorean triples are given by the formulas x2 - y2, 2xy, and x2 + y2. use the formulas for the pythagorean triples to find a right triangle with leg lengths of 16 and an odd number. show all of your work for full credit.

First of all, let me break down the formula: is always a Pythagorean triple because you have

So, for any you can choose (let's suppose ), these three numbers will always fall in the form , which is also the rule that works for right triangles. So, every time you choose two numbers , the legs will be and , while the hypotenuse will be .

We have to find a right triangles with legs 16 and an odd number. Well, the legs in the triple we are given are and , so we want one of this to be 16, and the other to be odd. But can't be odd, because it has a 2 factor in it. So, it must be 16: we have

The only ways we can choose two numbers such that their product is 8 are:

In the first case, the legs are

In the second case, the legs are

In this case both legs are even, so the only good choice is

So, the triangle we're working with has legs

and hypotenuse

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

it would be 3 ÷by 6 because the number on each side