To determine which statement is true, let's analyze the scenario.
- Let \( H \) be your house, \( B \) be the bank, and \( F \) be the farmer's market.
- The distance from your house to the farmer's market is stated to be 7 miles.
Since you need to stop at the bank before going to the farmer's market, the total distance you travel will be from your house to the bank and then from the bank to the farmer’s market.
The distance from your house to the bank (HB) plus the distance from the bank to the farmer's market (BF) can be expressed as:
\[ \text{Total distance} = HB + BF \]
Given that the distance from your house to the farmer’s market (HF) is 7 miles, the total distance (HB + BF) can be thought of in relation to the straight line distance HF.
Since you are traveling with an additional stop at the bank, the sum of HB and BF must be equal to or greater than the direct distance HF (7 miles). Therefore, we can conclude:
- \( HB + BF \geq 7 \) miles
From this, we can analyze the options:
a. The distance from your house to the bank and then the farmer's market is equal to 7 miles. (This is possible if the bank is exactly on the direct line between the house and the farmer's market. However, it cannot be guaranteed and is not necessarily true.)
b. The distance from your house to the bank and then the farmer's market is less than 7 miles. (This statement cannot be true as we established HB + BF ≥ 7 miles.)
c. The distance from your house to the bank and then the farmer's market is greater than 7 miles. (This is a possibility since we cannot guarantee that the bank is on the direct line to the farmer’s market.)
d. The distance from your house to the bank and then the farmer's market is 10 miles. (This is a specific distance and cannot be concluded without additional information about the specific distances involved.)
Thus, the statement that is always true is:
c. The distance from your house to the bank and then the farmer's market is greater than 7 miles.
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