Relations a) suppose m, a, be z and m > 0. prove that the following relation satisfy the properties of equivalence relation. (10pts) divides (a - b) m1(a-b) i. e. m
b) consider the following relations on the set of integers: r1: (r, y)l y} r2: (x, y)l> y} r3: {(x, y)l= y c r4: (r, y)z= y} r5: {(x, y)lz= y + 1} r6: {(r, y)|+y

The paint recipe also calls for 1/4 cup of food coloring. tyler says mrs.mcglashan will also need 6 cups of food coloring. do u agree or disagree? explain.

A.s.a.! similarity in right triangles, refer to the figure to complete this proportionc/a = a/? a.) cb.) hc.) rd.) s

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.