Which of the following conditions in a quadrilateral proves it is a parallelogram?

a.) opposite sides are parallel
b.) opposite sides are equal in length
c.) opposite angles are equal (angles "a" are the same, and angles "b" are the same)
d.) angles "a" and "b" add up to 180°, so they are supplementary angles.

The hypotenuse of a 45 -45 -90 triangle measure 7 square root 2 units

What two consecutive odd integers have a sum of -28

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.