Let's solve the given expression step by step:
[tex]\[
\frac{-2 \cdot (-30) + 0.5 \cdot 20}{4^2 - 6}
\][/tex]
### Step 1: Calculate [tex]\((-2) \cdot (-30)\)[/tex]
First, we handle the multiplication in the numerator:
[tex]\[
(-2) \cdot (-30) = 60
\][/tex]
### Step 2: Calculate [tex]\(0.5 \cdot 20\)[/tex]
Next, we handle the second multiplication in the numerator:
[tex]\[
0.5 \cdot 20 = 10
\][/tex]
### Step 3: Sum the results of the numerator
Now, add the results of the multiplications to get the complete numerator:
[tex]\[
60 + 10 = 70
\][/tex]
### Step 4: Calculate the denominator
Next, we calculate the denominator part. Start with the exponentiation:
[tex]\[
4^2 = 16
\][/tex]
Then, subtract 6 from the result:
[tex]\[
16 - 6 = 10
\][/tex]
### Step 5: Form the fraction and compute the final result
Now that we have both the numerator and the denominator, we can form the fraction and perform the division:
[tex]\[
\frac{70}{10} = 7
\][/tex]
### Step 6: Present the final result
The final result of the given expression is:
[tex]\[
7.0
\][/tex]
Thus, the step-by-step solution for the given expression [tex]\(\frac{-2 \cdot (-30) + 0.5 \cdot 20}{4^2 - 6}\)[/tex] is [tex]\(7.0\)[/tex].
