The number of plastic straws produced by a machine varies directly as the amount of time the machine is operating. if the machine produces 20,000 straws in 8 hours, how many straws can it produce in 50 hours?  

Given is the direct relationship between number of produced straws and the hours of operating machine.

Given that 20,000 straws are produced in 8 hours of machine's operation.

Let's assume that 'x' straws are produced in 50 hours of machine's operation.

Using the concept of proportions, x straws in 50 hours would be proportional to 2000 straws in 8 hours.

Hence, total 125,000 straws would be produced in 50 hours.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: