consider the following expression: -6 + 3 dot 5 ____ sqrt16 + 32 divided by 8

Question

which operator can be inserted to make the statement true?

<
>
=
or ⪯

Answer 1

Let's break down the expression step by step:

1. Evaluate the expression without an operator:

   • The given expression is: \[ -6 + 3 \cdot 5 \quad ___ \quad \sqrt{16} + \frac{32}{8} \]

2. Calculate each part:

   • Calculate \(3 \cdot 5\): \[ 3 \cdot 5 = 15 \]

   • So, the left side becomes: \[ -6 + 15 = 9 \]

   • Calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \]

   • Calculate \(\frac{32}{8}\): \[ \frac{32}{8} = 4 \]

   • Now, sum these values: \[ 4 + 4 = 8 \]

3. Now we have: \[ 9 \quad ___ \quad 8 \]

4. Determine the appropriate operator:

   • We need to determine which operator makes the statement true between:

     • \(<\)
     • \(>\)
     • \(=\)
     • \(⪯\)

   • Since \(9 > 8\), the appropriate operator to insert is \(>\).

So, the correct answer is: >