To find the coordinates of the point \( Q' \), we apply the translation given by the transformation \( (x,y) \to (x+7, y-5) \) to the coordinates of the point \( Q(0,6) \).
Starting with the coordinates of point \( Q \):
- \( x = 0 \)
- \( y = 6 \)
Applying the translation:
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For the \( x \)-coordinate, we calculate: \[ x' = x + 7 = 0 + 7 = 7 \]
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For the \( y \)-coordinate, we calculate: \[ y' = y - 5 = 6 - 5 = 1 \]
Thus, the coordinates of point \( Q' \) after the translation are: \[ Q' = (7, 1) \]
Therefore, the coordinates of \( Q' \) are \( \boxed{(7, 1)} \).