Construct a finite-state machine that models an old- fashioned soda machine that accepts nickels, dimes, and quarters. the soda machine accepts change until 35 cents has been put in. it gives change back for any amount greater than 35 cents. then the customer can push but- tons to receive either a cola, a root beer, or a ginger ale.

Given: hf || jk; hg ? jg prove: fhg ? kjg to prove that the triangles are congruent by asa, which statement and reason could be used as part of the proof? fgh ? kgj because vertical angles are congruent. jkg ? hfg because vertical angles are congruent. fhg ? jkg because right angles are congruent. hfg ? kjg because alternate interior angles are congruent.

Which of the following parabolas opens down?

Describe the end behavior of the function below. f(x)=(2/3)^x-2 a. as x increases, f(x) approaches infinity. b. as x decreases, f(x) approaches 2. c. as x increases, f(x) approaches -2. d. as x decreases, f(x) approaches negative infinity.