Misty has several pieces of construction paper that each measure 4 inches long and 9 inches wide. she needs to create the smallest possible square without cutting or overlapping. what is the measure of the square's side lengths?

We are given that the dimensions are 4 in x 9 in. To get the smallest possible square, first let us find for the LCM of 4 and 9.

4 = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36

9 = 0, 9, 18, 27, 36

We can actually see that 36 is the least common multiple.

Therefore the smallest possible square has a dimension of:

36 inches by 36 inches

The equation is y = $72.99 + $28.45(x - 1), where y is the monthly charge and x is the month in which it is calculated.

Step-by-step explanation:

Step 1; First we need to establish a relation between the difference in costs. For the first month it cost $72.99, during the second month, it costs $101.44 and in the third month, it costs $129.89. Difference in rates

Second months rate - First months rate = $101.44 - $72.99 = $28.45

Third months rate - Second months rate = $129.89 - $101.44 = $28.45.

So for every consecutive month, the charges increase by $28.45

Step 2; Now we develop an equation,

y = $72.99 + $28.45(x - 1), where y is the charge that month and x is the month in which it is calculated.

For x = 1, y = $72.99 + $28.45(1 - 1) = $72.99 + $28.45(0) = $72.99,

For x = 2, y = $72.99 + $28.45(x - 1) = $72.99 + $28.45(2 - 1) = $101.44,

For x = 3, y = $72.99 + $28.45(3 - 1) = $72.99 + $28.45(3-1) = $129.89.

So this is the equation to calculate the cost y the mobile provider charges in month x.