Gavin and Brianna want to know how far a mountain peak is from their houses. They measure the angles between the line of sight to the peak and to each other’s houses and carefully make the drawing shown. The actual distance between Gavin and Brianna’s houses is 1.5 miles. a. What is the actual distance of the mountain peak from Gavin’s house? Round your answer to the nearest tenth of a mile.
b. What is the actual distance of the mountain peak from Brianna’s house? Round your answer to the nearest tenth of a mile.

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?

Solve this 364x-64x=300x and 12(x2–x–1)+13(x2–x–1)=25(x2–x–1)

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.)