given: ∠1 ≅ ∠2
prove: a ∥ b

what is the missing statement in the proof?

∠1 ≅ ∠4

a ∥ b

∠1 ≅ ∠2

a ⊥ b

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

what’s the question?

the answer is 40.

proof:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.