A runner's racecourse has a total distance of . Race officials want to mark the course every with a flag, including one at the finish line. (The starting line does not need a flag.) How many flags are needed? First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.

Complete question :

A runner's racecourse has a total distance of 2.5 mi. Race officials want to mark the course every 200 yd with a flag, including one at the finish line. (The starting line does not need a flag. How many flags are needed?

22 flags

Step-by-step explanation:

Given that total distance = 2.5 miles

Marked distance = every 200 yards

Ratio of yard to miles:

1 mile = 1760 yards

Total distance in yards :

Note :

1 mile = 5280 feet

1 yard = 3 feet

Given that:

1 flag per 200 yards

Number of flags :

2.5 miles * (5280 / 1 ) * (1 /3) * (1 / 200) = 22 flags

Similarly ;

Since 1 mile = 1760 yards

Total distance in yards : (2.5 * 1760) = 4400 yards

Number of flags :

Total distance in yards / marked distance

= 4400 / 200

= 22 flags

We substitute

And simplify

Step-by-step explanation:

First we rearrange the equation -2=-x+x2-4 into standard form of a quadratic . This equation becomes where a=1, b=-1, and c=-2.

The formula is:

.

We substitute

And simplify