Prove or disprove each of the following statements. (a) there exists a prime number x such that x + 16 and x + 32 are also prime numbers. (b) va, b, c, m € z+, if a = b (mod m), then c = c (mod m). (c) for any positive odd integer n, 3]n or nº = 1 (mod 12). (d) there exist 100 consecutive composite integers.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. release your mouse button when the item is place. if you change your mind, drag the item to the trashcan. click the trashcan to clear all your answers. solve this quadratic equation using the quadratic formula. 2x2 - 2x=1 need asap

On traditional maps, earth is represented in a flat plane, or by euclidean geometry. however, a globe is a more accurate model that comes from elliptical geometry. how does a globe represent the fact that there are no parallel lines in elliptical geometry? the equator is not parallel to any other latitudinal lines. the north and south poles are never connected by a geodesic. the geodesics connecting the north and south poles never intersect. the geodesics connecting the north and south poles intersect at both of the poles.

Meghan has created a diagram of her city with her house, school, store, and gym identified. a. how far is it from the gym to the store? b. meghan also wants to walk to get some exercise, rather than going to the gym. she decides to walk along arc ab. how far will she walk? round to 3 decimal places.