Question
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7. \( t^{2}-12 w \div x \)

Ask by Parry Huang. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The expression simplifies to \( t^{2} - \frac{12w}{x} \).

Solution

Certainly! Let's analyze and simplify the expression you've provided: \[ t^{2} - 12w \div x \] **Interpreting the Expression:** The expression involves subtraction and division. According to the order of operations (PEMDAS/BODMAS), division should be performed before subtraction. Therefore, the expression is interpreted as: \[ t^{2} - \left(\frac{12w}{x}\right) \] **Simplified Form:** You can write the expression more clearly by using parentheses to indicate the order of operations: \[ t^{2} - \frac{12w}{x} \] **Combining into a Single Fraction (Optional):** If you prefer to combine the terms into a single fraction, you can rewrite the expression as follows: \[ \frac{t^{2}x - 12w}{x} \] **Final Simplified Forms:** 1. **With Separate Terms:** \[ t^{2} - \frac{12w}{x} \] 2. **As a Single Fraction:** \[ \frac{t^{2}x - 12w}{x} \] **Example Usage:** If you need to evaluate this expression for specific values of \( t \), \( w \), and \( x \), simply substitute the values into the simplified form. For instance, if \( t = 3 \), \( w = 2 \), and \( x = 4 \): \[ t^{2} - \frac{12w}{x} = 3^{2} - \frac{12 \times 2}{4} = 9 - \frac{24}{4} = 9 - 6 = 3 \] Feel free to provide more context or specify if you need further assistance with this expression, such as solving for one of the variables or graphing the equation!

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Extra Insights

This expression could represent various mathematical or physical concepts depending on the context. For instance, if \(t\), \(w\), and \(x\) are variables representing time, work, and a certain measure (like distance or effort), this expression could relate to a specific scenario in physics or engineering where you're modeling motion, energy, or force. When working with such expressions, always remember the order of operations (PEMDAS/BODMAS) to avoid common mistakes. Misplacing a division or forgetting to square a term can lead to incorrect results. Double-check your calculations and ensure you're applying the right mathematical principles!

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