Consider the equation x^2+(y-2)^2 = 1 and the relation “(x, y) r (0, 2)”, where r is read as “has distance 1 of”. for example, “(0, 3) r (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. this relation can also be read as “(x, y) belongs to the circle of radius 1 with center (0, 2)”. in other words: “(x, y) satisfies this equation if, and only if, (x, y) r (0, 2)”. does this equation determine a relation between x and y ? can the variable x can be seen as a function of y, and y be seen as a function of x ? what are the domains for these two functions? what are the graphs of these two functions? are there points of the coordinate axes that relate to (0, 2) by means of r ? your discussion should be a minimum of 250 words in length and not more than 750 words.

Leo has b boxes of pencils. each box contains 6 pencils. he has a total of 42 pencils. the equation that represents this situation the value of b that makes the equation true the first one is b+6=42,6b=42,b=42+6,or 42b=6 the second one are 7,836 48

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?

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.