2x+3y + 2z = 0
5x – 3y +4=1
7x+9y-4z=11

Danny draws a transversal, t, on two parallel lines ab and cd, as shown below: he makes the following table to prove that the alternate interior angles are equal: which is the missing justification? (6 points) corresponding angles formed by a transversal on parallel lines are supplementary. corresponding angles formed by a transversal on parallel lines are congruent. co-interior angles formed by a transversal on parallel lines are congruent. co-exterior angles formed by a transversal on parallel lines are congruent.

Find the smallest number by which the given number should be divided to make a perfect cube(with steps or the answer will get reported) a.108 b.2187

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.)