To simplify the expression \((9-2)+(4\sqrt{18})-32\), we follow the order of operations:
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Parentheses: First, calculate the value inside the parentheses: \[ 9 - 2 = 7 \] Now the expression looks like: \[ 7 + (4\sqrt{18}) - 32 \]
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Square Roots: Next, we will compute \(4\sqrt{18}\). First, simplify \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9}\sqrt{2} = 3\sqrt{2} \] Now substitute back into the expression: \[ 4\sqrt{18} = 4(3\sqrt{2}) = 12\sqrt{2} \] The expression is now: \[ 7 + 12\sqrt{2} - 32 \]
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Addition and Subtraction: Combine the constant terms: \[ 7 - 32 = -25 \] Now the expression is: \[ -25 + 12\sqrt{2} \]
Since there are no further operations to simplify, the final expression is: \[ -25 + 12\sqrt{2} \]
This result does not match any of the responses given. Depending on the context of the answers provided, it seems the expression should be simplified to a numeric value. Let's evaluate \(12\sqrt{2}\).
Using an approximate value of \(\sqrt{2} \approx 1.414\): \[ 12\sqrt{2} \approx 12 \times 1.414 \approx 16.968 \] Thus, we calculate: \[ -25 + 16.968 \approx -8.032 \]
However, there are no options that align with the specific numeric value achieved through the steps. The closest answer can be interpreted differently based on simplification.
If we focus only on evaluating constants and ignoring the radical, the numerical combinations yield values typically not represented. Thus, further context or possible errors in measurement might be needed. However, if no clear answer emerges and order of operations is accurately followed, we assert that: \[ -25 + 12\sqrt{2} \] is an appropriate response until re-evaluation options present clearer guidance.