The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:

Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB _. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which phrase best completes the student's proof?

are congruent by the AAS postulate
are congruent by the ASA postulate
form a pair of alternate interior angles that are congruent
form a pair of vertical angles that are congruent

answer: 180

step-by-step explanation:

12-2=10

20-2=18

10x18=180

mr. graef told us it is 13 pints

step-by-step explanation:

what is the answer?

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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