What is the following quotient? StartFraction StartRoot 6 EndRoot + StartRoot 11 EndRoot Over StartRoot 5 EndRoot + StartRoot 3 EndRoot EndFraction StartFraction StartRoot 30 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot + StartRoot 33 EndRoot Over 8 EndFraction StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2 EndFraction Seventeen-eighths Negative five-halves

(05.08a)triangle abc is transformed to similar triangle a′b′c′ below: a coordinate plane is shown. triangle abc has vertices a at 2 comma 6, b at 2 comma 4, and c at 4 comma 4. triangle a prime b prime c prime has vertices a prime at 1 comma 3, b prime at 1 comma 2, and c prime at 2 comma 2. what is the scale factor of dilation? 1 over 2 1 over 3 1 over 4 1 over 5

Solve the system of equations using the substitution method. {y=−3x+7x=−2y−16 enter your answers in the boxes.

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.)