To analyze the predictions based on the linear model \( y = 34x + 2 \), we need to interpret the variables:
- \( y \) represents the number of miles the car can travel,
- \( x \) represents the number of gallons of gas.
Now we can evaluate the given options by substituting the values of \( x \) into the equation to see if the predictions hold true.
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For 15 gallons: \[ y = 34(15) + 2 = 510 + 2 = 512 \text{ miles} \] This means a car can indeed go over 500 miles on 15 gallons of gas.
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For 20 gallons: \[ y = 34(20) + 2 = 680 + 2 = 682 \text{ miles} \] This means a car can indeed go over 700 miles on 20 gallons of gas, as it travels 682 miles.
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For 3 gallons: \[ y = 34(3) + 2 = 102 + 2 = 104 \text{ miles} \] This means a car will go more than 100 miles on 3 gallons of gas, contrary to the statement that it will go less than 100 miles.
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For 12 gallons: \[ y = 34(12) + 2 = 408 + 2 = 410 \text{ miles} \] This means a car can go exactly 400 miles is false; it can actually go 410 miles on 12 gallons.
Based on these calculations, the correct predictions from the options provided are:
- A car can go over 500 miles on 15 gallons of gas.
- With 20 gallons of gas, a car can travel over 700 miles.
Both statements are true. However, if you must choose one option based on the original question format, the first one regarding 15 gallons directly asserts that it can go over 500 miles, which is a solid prediction based on the model.