Suppose you owe 10 dollars to a friend. Each week you pay your friend at least 1 dollar back. Sometimes however you might pay your friend back 2 dollars in a week and other times you might pay your friend 5 dollars in a week. How many different payment sequences are possible

step-by-step explanation:

consider the parallelogram shown in the attached image.

in the parallelogram hijk, the length of hk is given as,

from the properties of parallelogram we know that the opposite sides of a parallelogram are parallel to each other and are equal in measure.

therefore, the length of the side ij must be equal to the length of the side hk and that is .

hence, the expression for the length of ij confirms that hijk is a parallelogram.