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An inverted triangle shows the upper left vertex labeled as house, with a side marked 5 miles leading to the lower right vertex labeled as farmer's market. The third vertex at the bottom is labeled bank.

The diagram shows the distance between your house, the bank, and the farmer’s market. You need to stop at the bank before going to the farmer’s market. Given the information in the diagram, identify which statement is true.

(1 point)
Responses

The distance from your house to the bank and then the farmer’s market is 8 miles.
The distance from your house to the bank and then the farmer’s market is 8 miles.

The distance from your house to the bank and then the farmer’s market is less than 5 miles.
The distance from your house to the bank and then the farmer’s market is less than 5 miles.

The distance from your house to the bank and then the farmer’s market is equal to 5 miles.
The distance from your house to the bank and then the farmer’s market is equal to 5 miles.

The distance from your house to the bank and then the farmer’s market is greater than 5 miles.

1 answer

To determine the correct statement regarding the distances between your house, the bank, and the farmer's market, let’s analyze the information provided in the diagram description.

  1. House to Bank: Let's denote the distance from your house to the bank as \( x \).
  2. House to Farmer's Market: The distance from your house to the farmer's market is given as 5 miles.
  3. Bank to Farmer's Market: Since you need to stop at the bank before going to the farmer's market, the total distance traveled would be the sum of the distances from your house to the bank and then from the bank to the farmer's market.

However, we do not have the distance from the bank to the farmer's market explicitly listed in the information provided. Therefore, we can analyze the given options based on the knowledge we have.

  • If the distance from your house to the bank \( x \) is less than or equal to 5 miles:
    • The statement that the total distance is less than 5 miles cannot be true, as that would imply you can't reach the bank and then the market within the distance constraint if \( x \) is already 5 miles.
  • The statement that the total distance is equal to 5 miles is also not possible since the distances must add up (bank to market distance not defined).
  • The first statement implies the bank is 3 miles away (as 5+3=8), which still doesn't allow a valid conclusion based solely on the given data.

Thus:

  • The distance from your house to the bank and then to the farmer's market cannot logically be less than or equal to 5, so the only valid conclusion, in terms of basics, is that if they are both part of a triangle formation and given the positioning hint, one can conclude contextually:

"The distance from your house to the bank and then the farmer’s market is greater than 5 miles."

This is because if the distance to the farmer's market alone is 5 miles without knowing the distance to the bank, the total journey must logically exceed that.

So the correct answer is:

The distance from your house to the bank and then the farmer’s market is greater than 5 miles.