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.

Benjamin is making bow ties. how many 1/2yards lomg bow ties can he make if he has 18 feet of fabric?

Examine the paragraph proof. which theorem does it offer proof for? prove jnm – nmi according to the given information in the image. jk | hi while jnm and lnk are vertical angles. jnm and lnk are congruent by the vertical angles theorem. because lnk and nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, jnm is congruent to nmi by the transitive property of equality alternate interior angles theorem gorresponding angle theorem vertical angle theorem o same side interior angles theorem

(05.02) mr. morris is going to save money and replace his sailboat's mainsail himself. he must determine the area of the mainsail in order to buy the correct amount of material. calculate the area of the parallelogram to determine how much material should be purchased. be sure to explain how to decompose this shape into rectangles and triangles. describe their dimensions and show your work.