To find the new coordinates \( E' \) after translating the point \( E(7, 0) \) right by 20 units and down by 19 units, we perform the following calculations:
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Translate right by 20: This means we add 20 to the x-coordinate. \[ x' = 7 + 20 = 27 \]
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Translate down by 19: This means we subtract 19 from the y-coordinate. \[ y' = 0 - 19 = -19 \]
Therefore, the new coordinates \( E' \) are: \[ E' = (27, -19) \]
In parentheses, the final answer is: \[ \boxed{(27, -19)} \]