What is the length of the diagonal from vertex J to vertex L in the quadrilateral below?

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?

[15 points]find the least common multiple of the expressions: 1. 3x^2, 6x - 18 2. 5x, 5x(x +2) 3. x^2 - 9, x + 3 4. x^2 - 3x - 10, x + 2 explain if possible

Line segment eg is partitioned by point f in the ratio 1: 1. point e is at e (0, 4), and point f is at (1, 3). what are the coordinates of point g? (−1, 5) (2, 2) (3, 1) (4, 0)