Answer:
46.9 times
Step-by-step explanation:
First, we can calculate how many feet it takes to run around the field. To find the perimeter of a rectangle, we can use the formula
2* length + 2 * width. With the length being 450 and the width being 225 here, we can say that
2*450 + 2 * 225 = 1350 feet
Therefore, Andrew runs 1350 feet each time he runs around the field. Next, we need to figure out how much 1350 feet goes into 12 miles as we want to find how many times Andrew runs around the field to get to 12 miles. This can be represented by
12 miles/1350 feet
One thing that we can do here is multiply the fraction by 1 to keep it the same. Because 1 mile = 5280 feet, we can say that
1 mile/5280 feet = 1 = 5280 feet/1 mile. Therefore, it would be safe to multiply
12 miles/1350 feet by 1 = 5280 feet/1 mile. Note that feet is on the bottom in the first fraction (12 miles/1350 feet) and on the top in the second (5280 feet/1 mile) so they will cancel out. Similarly, miles are on top in the first and bottom in the second. We then have
12 miles/1350 feet * 5280 feet/1 mile =63360/1350 ≈ 46.9
A parallel line has the same slope as the original line. So in this case the slope of the line is also 3/4. Now how do we know if it intersects the point? We need to adjust the y intercept.
Currently, we know the equation of the line is y= 3/4 x + b, where b is the thing we are looking for. We also have a point, which supplies the x and y. Plug that in and solve for b
-2 = (3/4)*(12) + b
You'll get b= -11
So the equation of the parallel line intersecting the point given is y= 3/4x -11.
I am assuming that the slope is 3/4 based on the way you formatted the original equation, but it's the same steps if the slope is different.
