Which triangle’s area can be calculated using the trigonometric area formula?

triangle a b c is shown. the length of a c is 28, the length of c b is 24, and the length of a b is 16.
triangle d e f is shown. the length of e f is 20. angle f d e is 34 degrees and angle d e f is 108 degrees.
triangle g h j is shown. the length of g h is 17 and the length of g j is 22. angle h j g is 47 degrees.

Which expression is equivalent to 2x^2+2x-4/2x^2-4x+2

Aflagpole broke in a storm. it was originally 8 1 81 feet tall. 2 8 28 feet are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground some distance away. how far away is the end of the pole from the base of the pole along the ground?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)