At what point(s) do these graphs intersect? y+x^2=3x-5 and y=4x+1 Seth’s solution:

y=x^2=3x-5

y=4x+1

x^2+3x-5=4x+1

x^2-x-6=0

x=3 and x=-2

The graphs intersect at (-2,0) and (3,0).

Is Seth’s solution correct? Explain.

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.)