On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, 2), (2, 4), (2, 1). Triangle A prime B prime C prime has points (negative 2, 5), (negative 4, 2), (negative 1, 2). Triangle A double-prime B double-prime C double-prime has points (negative 2, negative 5), (negative 4, negative 2), (negative 1, negative 2). Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"? 90 degree rotation about point 0 composition reflection across the x-axis Reflection across the x-axis composition 90 degree rotation about point 0 180 degree rotation about point 0 composition reflection across the x-axis Reflection across the x-axis composition 180 degree rotation about point 0

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Acaterer charges $500 plus $30 per guest to cater a wedding. walt and traci don't want to spend more than $8000 on catering. write and solve an inequality in terms of the number of guests, g, that can be invited. a) 30g ? 8000; g ? 267 b) 500g < 8000; g < 16 c) 500 + 30g < 8000; g < 250 d) 500 + 30g ? 8000; g ? 250

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.