The relationship between a distance measured in miles, m, and the same distance measured in feet, f, can be described by the equation f = 5280m. Using this information, complete th... The relationship between a distance measured in miles, m, and the same distance measured in feet, f, can be described by the equation f = 5280m. Using this information, complete the following table with the measurement in miles and feet. Is there a proportional relationship between a distance measured in miles and the same distance measured in feet?

Question image

Understand the Problem

The question is asking to complete a table that relates distances in miles to feet based on a given equation, and to determine if there is a proportional relationship between these two measurements.

Answer

Yes, there is a proportional relationship between distance in miles and the same distance measured in feet.
Answer for screen readers

The completed table is:

distance in miles, ( m ) distance in feet, ( f )
1 5280
5 26400
8 42240
10 52800

Yes, there is a proportional relationship.

Steps to Solve

  1. Understanding the Equation The relationship between miles and feet is given by the equation ( f = 5280m ). Here, ( f ) represents the distance in feet, and ( m ) represents the distance in miles.

  2. Calculate Distance in Feet for 1 Mile Using the equation for ( m = 1 ): [ f = 5280 \times 1 = 5280 \text{ feet} ] This fills in the first row of the table.

  3. Calculate Distance in Feet for 5 Miles Now for ( m = 5 ): [ f = 5280 \times 5 = 26400 \text{ feet} ] This fills in the second row of the table.

  4. Check Given Values for 42,240 and 52,800 Feet To see if ( 42,240 ) and ( 52,800 ) are valid:

    • For ( 42,240 ): [ \frac{42240}{5280} = 8 \implies m = 8 \text{ miles} ]
    • For ( 52,800 ): [ \frac{52800}{5280} = 10 \implies m = 10 \text{ miles} ] This indicates both values correspond to specific distances in miles.
  5. Determine Proportional Relationship To check if the relationship is proportional, see if the ratio ( \frac{f}{m} ) is constant:

  • For ( m = 1 ), ( \frac{5280}{1} = 5280 )
  • For ( m = 5 ), ( \frac{26400}{5} = 5280 )
  • For ( m = 8 ), ( \frac{42240}{8} = 5280 )
  • For ( m = 10 ), ( \frac{52800}{10} = 5280 )

Since the ratio is constant, the relationship is proportional.

The completed table is:

distance in miles, ( m ) distance in feet, ( f )
1 5280
5 26400
8 42240
10 52800

Yes, there is a proportional relationship.

More Information

The equation ( f = 5280m ) shows a direct relationship between miles and feet. This means for every mile, there are 5280 feet, which is a standard conversion.

Tips

  • Miscalculating the multiplication when finding ( f ) for each mile.
  • Forgetting to check if the ratios ( \frac{f}{m} ) are consistent to determine proportionality.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser