We are asked to find the area of the rectangle that has side lengths of 3/4 yard and 5/6 yard.
We know that area of rectangle is width times length.
To find the area of the given rectangle we will multiply both side lengths as:
Therefore, the area of the given rectangle would be 
square yards.
Find the difference in the y-coordinates: -3 - 1 = -4
Find the difference in the x-coordinates in the same order: 2 - 5 = -3
Divide the difference in y by the difference in x: slope = (-4)/(-3)
Reduce the fraction: slope = 4/3
The unit rate of speed is 52.5 miles per hour
<em><u>Solution:</u></em>
Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21 hours and 15 minutes
We know that, 1 hour = 60 minutes
21 hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours
So they drive 1115.625 miles in 21.25 hours
To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken
unit rate of speed means miles driven in 1 hour
So the unit rate of speed is 52.5 miles per hour
(a) x = 4
First, let's calculate the area of the path as a function of x. You have two paths, one of them is 8 ft long by x ft wide, the other is 16 ft long by x ft wide. Let's express that as an equation to start with.
A = 8x + 16x
A = 24x
But the two paths overlap, so the actual area covered will smaller. The area of overlap is a square that's x ft by x ft. And the above equation counts that area twice. So let's modify the equation by subtracting x^2. So:
A = 24x - x^2
Now since we want to cover 80 square feet, let's set A to 80. 80 = 24x - x^2
Finally, let's make this into a regular quadratic equation and find the roots.
80 = 24x - x^2
0 = 24x - x^2 - 80
-x^2 + 24x - 80 = 0
Using the quadratic formula, you can easily determine the roots to be x = 4, or x = 20.
Of those two possible solutions, only the x=4 value is reasonable for the desired objective.
(b) There were 2 possible roots, being 4 and 20. Both of those values, when substituted into the formula 24x - x^2, return a value of 80. But the idea of a path being 20 feet wide is rather silly given the constraints of the plot of land being only 8 ft by 16 ft. So the width of the path has to be less than 8 ft (the length of the smallest dimension of the plot of land). Therefore the value of 4 is the most appropriate.
