Secant TQ and tangent TR intersect at point T. Chord SR and chord PQ intersect at point V. Find the values of x and y. If necessary, round to the nearest tenth.

Abag contains 4 red, 7 blue and 5 yellow marbles. event a is defined as drawing a yellow marble on the first draw and event b is defined as drawing a blue marble on the second draw. if two marbles are drawn from the bag, one after the other and not replaced, what is p(b|a) expressed in simplest form? a. 7/16 b. 7/15 c. 14/16 d. 14/15

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

Lian is deciding which of two gyms to join. each gym charges a monthly rate plus a one-time membership fee. lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. in her work, she substituted an expression for one variable and solved for the other. this resulted in the equation 75 = 75. what can lian conclude? one gym charges $75 per month. each gym charges $75 per month both gyms charge the same monthly rate and the same membership fee. both gyms charge the same monthly rate, but not the same membership fee.