Determine whether the relation r on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ r if and only if:

(a) x + y = 0, (b) x = ±y, (c) x − y is a rational number, (d) x = 2y, (e) xy ≥ 0, (f) xy = 0, (g) x = 1, (h) x = 1 or y = 1.

Fiona and her friends are playing a game by guessing where a coin will land when it is randomly dropped inside the square shown below. fiona guesses that the coin is likely to land in the blue area. which explains whether or not fiona is correct and why?

Pyotr tchaikovsky sporting goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 on the newest version of an air hockey game set. if the air hockey game set costs pyotr tchaikovsky sports $49.32, find the selling price, the markup, and the net profit.

The graph of a hyperbola is shown. what are the coordinates of a vertex of the hyperbola? (0, −4) (−3, 0) (0, 0) (0, 5)