Grant Chen
05/03/2023 · Middle School
\( \left. \begin{array} { l } { \theta ^ { 2 } = 1 ^ { 2 } \quad ( 6 = 1 ) ^ { 2 } } \\ { \theta ^ { 2 } = 1 ^ { 2 } = 95 } \\ { ( 0 - 1 ) ^ { 2 } = \square } \end{array} \right. \)
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Tutor-Verified Answer
Step-by-step Solution
Let's analyze the equations provided step by step.
1. The first equation is \( \theta^2 = 1^2 \). This simplifies to \( \theta^2 = 1 \). Therefore, \( \theta = 1 \) or \( \theta = -1 \).
2. The second equation is \( (6 = 1)^2 \). This expression is not mathematically valid as it stands, since \( 6 \neq 1 \). However, if we interpret it as \( (6 - 1)^2 \), we get \( 5^2 = 25 \).
3. The next equation states \( \theta^2 = 1^2 = 95 \). This is also incorrect because \( 1^2 = 1 \), not 95. Therefore, this equation does not hold true.
4. The last equation is \( (0 - 1)^2 = \square \). This simplifies to \( (-1)^2 = 1 \). Thus, \( \square = 1 \).
In summary, the valid conclusions we can draw from the equations are:
- \( \theta^2 = 1 \) implies \( \theta = 1 \) or \( \theta = -1 \).
- The expression \( (0 - 1)^2 \) evaluates to \( 1 \).
If you have any specific questions or need further clarification, feel free to ask!
Quick Answer
- \( \theta^2 = 1 \) implies \( \theta = 1 \) or \( \theta = -1 \).
- \( (0 - 1)^2 = 1 \).
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