To evaluate the expression \( h^2 + g - 13 \) with \( g = -3 \) and \( h = -7 \), we can follow these steps:
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Calculate \( h^2 \): \[ h^2 = (-7)^2 = 49 \]
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Now substitute \( h^2 \) and \( g \) into the expression: \[ h^2 + g - 13 = 49 + (-3) - 13 \]
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Simplify the expression: \[ 49 - 3 - 13 = 46 - 13 = 33 \]
Thus, the final result is: \[ \boxed{33} \]