Which expressions have a value of 100 when $m=5$? Select all that apply.
We are given two algebraic expressions and asked to determine which one evaluates to \(100\) when \(m = 5\). The expressions are:
Our goal is to substitute \(m = 5\) into each expression, perform the arithmetic, and check if the result is \(100\).
We substitute \(m = 5\) into expression \(A = 2m^2 + 50\):
\[A = 2(5)^2 + 50\]
First, calculate the square: \(5^2 = 25\).
Then, multiply by \(2\): \(2 \times 25 = 50\).
Finally, add \(50\): \(50 + 50 = 100\).
Since the result is \(100\), expression \(A\) is one of the correct choices.
Now, we substitute \(m = 5\) into expression \(B = (2m)^2 + 50\):
\[B = (2 \times 5)^2 + 50\]
First, perform the multiplication inside the parentheses: \(2 \times 5 = 10\).
Then, calculate the square: \(10^2 = 100\).
Finally, add \(50\): \(100 + 50 = 150\).
Since the result is \(150\), which is not \(100\), expression \(B\) is not a solution to the problem.
We have tested both expressions. Expression \(A = 2m^2 + 50\) results in \(100\) when \(m=5\), while expression \(B = (2m)^2 + 50\) results in \(150\). Therefore, only expression \(A\) evaluates to \(100\). The final answer is \(\boxed{A}\).
This problem demonstrates the importance of the order of operations in algebraic expressions. In real-world scenarios, such as calculating costs or growth, misplacing parentheses can lead to significant errors. For example, if you are designing a pricing model where you double the base quantity before squaring versus squaring first, the outcomes will differ wildly. Understanding this helps ensure precision in modeling and financial planning.