Which expression has a value of 10?
The Correct Answer and Explanation is:
To determine which expression has a value of 10, we need to analyze different types of mathematical expressions and evaluate their values. Common forms of expressions include linear equations, polynomial expressions, exponential expressions, and logarithmic expressions, among others.
Example Expressions
- Linear Expression: ( 2x + 4 = 10 )
- To solve for ( x ):
[
2x + 4 = 10
]
[
2x = 10 – 4
]
[
2x = 6 \quad \Rightarrow \quad x = 3
] - When ( x = 3 ), the expression equals 10.
- Polynomial Expression: ( x^2 – 6x + 9 = 10 )
- Rearranging gives:
[
x^2 – 6x + 9 – 10 = 0 \quad \Rightarrow \quad x^2 – 6x – 1 = 0
] - Solving this quadratic using the quadratic formula:
[
x = \frac{6 \pm \sqrt{(-6)^2 – 4 \cdot 1 \cdot (-1)}}{2 \cdot 1} = \frac{6 \pm \sqrt{36 + 4}}{2} = \frac{6 \pm \sqrt{40}}{2}
] - This will yield two possible ( x ) values where the expression evaluates to 10.
- Exponential Expression: ( 2^x = 10 )
- To solve for ( x ):
[
x = \log_2(10)
] - Evaluating ( \log_2(10) ) gives an approximate value of ( 3.32193 ), indicating that ( 2^{3.32193} ) is indeed approximately 10.
Conclusion
Each of these expressions can be manipulated or solved to show that they can yield the value of 10 under certain conditions. Therefore, when determining which expression has a value of 10, one must first identify the context of the expression and then perform the necessary calculations or manipulations. The key takeaway is that various mathematical expressions can be equal to 10 by appropriately solving for the variables involved.