Using the equation f = 5280m, complete the table with the measurement in miles and feet. Is there a proportional relationship between a distance measured in miles and the distance... Using the equation f = 5280m, complete the table with the measurement in miles and feet. Is there a proportional relationship between a distance measured in miles and the distance measured in feet?

Question image

Understand the Problem

The question is asking to complete a table that relates distances in miles to corresponding distances in feet using the equation f = 5280m. This involves calculating the distance in feet for given distances in miles and determining if there is a proportional relationship.

Answer

- 5280, 21120, 26400, 52800; Yes.
Answer for screen readers
  • For 1 mile: 5280 feet
  • For 4 miles: 21120 feet
  • Distance in feet for 5 miles: 26400 feet
  • Distance in feet for 10 miles: 52800 feet
  • Yes, there is a proportional relationship.

Steps to Solve

  1. Analyzing the Formula
    The formula given is $f = 5280m$, where $f$ is the distance in feet and $m$ is the distance in miles. This means that for every mile, there are 5280 feet.

  2. Calculating for 1 Mile
    To find the distance in feet for 1 mile: $$ f = 5280 \cdot 1 = 5280 \text{ feet} $$

  3. Calculating for 4 Miles
    Now for 4 miles: $$ f = 5280 \cdot 4 = 21120 \text{ feet} $$

  4. Filling in Missing Distances
    You already have $26400$ feet and $52800$ feet filled in, so we can solve for the miles by dividing:

    • For $26400$ feet: $$ m = \frac{26400}{5280} = 5 \text{ miles} $$

    • For $52800$ feet: $$ m = \frac{52800}{5280} = 10 \text{ miles} $$

  5. Identifying Proportional Relationship
    A proportional relationship exists if the ratio of $f$ to $m$ is constant. Here, the ratio is always $5280$. Therefore, there is a proportional relationship.

  • For 1 mile: 5280 feet
  • For 4 miles: 21120 feet
  • Distance in feet for 5 miles: 26400 feet
  • Distance in feet for 10 miles: 52800 feet
  • Yes, there is a proportional relationship.

More Information

This problem demonstrates how to convert between miles and feet using a constant factor. It shows that the relationship between the two measurements is linear and proportional, as described by the formula.

Tips

  • Forgetting to multiply by $5280$ when converting from miles to feet.
  • Miscalculating the division when finding miles from feet.
Thank you for voting!
Use Quizgecko on...
Browser
Browser