Define a relation Q on the set Rx R as follows. For all ordered pairs (w, x) and (y, z) in RxR, (w, x) Q (y, z) = x= z. (a) Prove that is an equivalence relation. To prove that is an equivalence relation, it is necessary to show that is reflexive, symmetric, and transitive. Proof that Q is an equivalence relation: (1) Proof that Q is reflexive: Construct a proof by selecting sentences from the following scrambled list and putting them in the correct order.
a. By the reflexive property of equality, x = x
b. By definition of Q, (w, x) = (w, x).
c. By the symmetric property of equality, w = w.
d. By the reflexive property of equality, w = w.
e. By the symmetric property of equality, x = x.

Cthe residual plot for model 1 has a non random pattern and is a good fit for the data

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12