To determine the team's total progress, we can calculate the net yardage by combining the results of each play.
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The team gained 12 yards on the first play: \[ +12 \text{ yards} \]
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The team lost 4 yards on the second play: \[ -4 \text{ yards} \]
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The team gained 7 yards on the third play: \[ +7 \text{ yards} \]
Now, we can sum these values to find the total progress: \[ 12 + (-4) + 7 \]
Calculating this step-by-step:
- Calculate \(12 - 4\): \[ 12 - 4 = 8 \]
- Now add 7 to the result: \[ 8 + 7 = 15 \]
Thus, the team's total progress after these plays is: \[ \boxed{15} \text{ yards} \]