What is the value of the variable and BC if B is between A and C. AB=4x BC=5x AB=16

To find the value of the variable `x` and the length of segment `BC`, we can use the given information that "B is between A and C" and the lengths of segments AB and BC.

Since B is between A and C, we can assume that the segment BC connects B to C.

Given:
AB = 4x (length of segment AB)
BC = 5x (length of segment BC)
AB = 16 (length of segment AB, given another time)

To solve for the value of `x`, we can set the two expressions of AB equal to each other:

4x = 16

Dividing both sides of the equation by 4, we get:

x = 16/4

Simplifying further:

x = 4

Now that we know the value of `x`, we can substitute it back into the expression for BC:

BC = 5x = 5 * 4 = 20

Therefore, the value of the variable `x` is 4, and the length of segment BC is 20.