To get a human or AI tutor to help you, click Register
Sample Question 2:
Step 1: Substitute the given values, \(5\), \(3\), and \(6\), into the defined operations.
The operation \(5 \, \blacklozenge \, 3\) translates to \(5^2 - 3^2\).
Step 2: Solve for \(5^2 - 3^2\). This results in \(25 - 9\), which simplifies to \(16\).
Step 3: Plug the result of \(5 \, \blacklozenge \, 3\) into the second operation \(\bigstar \). Therefore, our equation is now \(16 \, \bigstar \, 6\), which translates to \((16 - 6)^2\).
Step 4: Solve for \((16 - 6)^2\). This results in \(10^2\), which simplifies to \(100\).
So, \((5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 100\), which corresponds to answer choice \(\boxed{\textbf{(D) } 100}\).
Consider these two operations: 
What is the value of \((5 \, \blacklozenge \, 3) \, \bigstar \, 6?\)
\(\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220\)
Answer Keys
Question 2: DSolutions
Question 2Step 1: Substitute the given values, \(5\), \(3\), and \(6\), into the defined operations.
The operation \(5 \, \blacklozenge \, 3\) translates to \(5^2 - 3^2\).
Step 2: Solve for \(5^2 - 3^2\). This results in \(25 - 9\), which simplifies to \(16\).
Step 3: Plug the result of \(5 \, \blacklozenge \, 3\) into the second operation \(\bigstar \). Therefore, our equation is now \(16 \, \bigstar \, 6\), which translates to \((16 - 6)^2\).
Step 4: Solve for \((16 - 6)^2\). This results in \(10^2\), which simplifies to \(100\).
So, \((5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 100\), which corresponds to answer choice \(\boxed{\textbf{(D) } 100}\).