Contains the length of the directed edge ( x , y ) in the intersection of row x and column y in a digraph with vertex set { a , b , c , d , e , f } . for example, w ( b , d ) = 21 . (on the other hand, w ( d , b ) = 10 . ) use this data and dijkstra's algorithm to find the distance from a to each of the other vertices and a directed path of that length from a .

Is each relation a function? if so, state whether it is one-to-one or many-to-one. 3. (-4,7), (-3,5), (1,4), (3,-8), (5,-11) 4. (-4,8), (-2,4), (0,1), (2,4), (4,8) 5. (-2, 1), (-2,3), (0,-3), (1,4), (3,1)

Terri makes a quilt using three sizes of fabric squares the side lenght of each fabric square is the square root of the area

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?