Diophantus of Alexandria (c. 275) was an outstanding Greek mathematician who wrote extensively on quadratic equations. He also collected and catalogued all of the algebra the Greeks had achieved. Nothing is really known about his life, when or where he lived, or how he died. All that is known about him comes from an algebra problem inscribed on his tombstone. The problem is as follows: Diophantus spent 1 of his life in childhood, 1 as a youth, and 1 more as a 6 12 7 bachelor. Five years after his marriage was born a son who died four years before his father at half the age at which his father died. How old was Diophantus when he died?

What is the length of the unknown leg in the right triangle ?

Cody started biking to the park traveling 15 mph, after some time the bike got a flat so cody walked the rest of the way, traveling 4 mph. if the total trip to the park took 6 hours and it was 46 miles away, how long did cody travel at each speed? solve using rate times time= distance

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.