Prove the identity: (cosx + cosy)^2 + (sinx - siny)^2 = 2 + 2 cos (x+y).

John checked his watch and said that it is thursday, 7 am. what will the day and time be 2006 hours plzzz i will give you 100 points

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.)

Atriangle has side lengths of x, x+11, and 3x+5. what is the perimeter? question 1 options: 3x2+38x+55 3x3+38x2+55x 5x+16 4x+16