The lengths of two sides of a triangle are 20 cm and 32 cm.
Explain why the third side of the triangle can or cannot have a length of 10 cm

No

Step-by-step explanation:

By the Triangle Inequality Theorem, for sides a, b, and c of a triangle:

a + b > c

a + c > b

b + c > a

Here, we already have two sides of lengths 20 and 32. We want to see if the third side can be 10 cm. Suppose a = 32, b = 20, and c = 10. According to the Triangle Inequality Theorem:

20 + 32 >? 10  ⇒  52 > 10       that's good

32 + 10 >? 20  ⇒  42 > 20       that's also good

20 + 10 >? 32  ⇒  30 > 32       this is false

So, the third side cannot be 10 because that would violate the theorem.

Hope this helps!

answer: h

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.