Where is Point A’ located after quadrilateral ABCD has transformed using the rule: (x, y) → (-x, y - 8)? Show your work.

You are assembling pieces of an iron gate to complete a fence. the finished gate will look like the one below. in order to assemble the gate it is important to under how the pieces are related. part 1: how are pies 1 and 2 in the archway related? part 2: how are the rectangular sections 5 and 6 in the center of the gate related to each other?

Solve each quadratic equation by factoring and using the zero product property. 14x - 49 = x^2

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.)