Let's evaluate the given expression step-by-step for [tex]\( a = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]. The expression is:
[tex]\[ 12 + \left[ 2 - \left( 4 \cdot a^2 \right) \right] \div 7 + b \][/tex]
### Step 1: Calculate [tex]\( 4 \cdot a^2 \)[/tex]
Given [tex]\( a = 5 \)[/tex],
[tex]\[ 4 \cdot a^2 = 4 \cdot (5^2) = 4 \cdot 25 = 100 \][/tex]
### Step 2: Calculate [tex]\( 2 - (4 \cdot a^2) \)[/tex]
[tex]\[ 2 - 100 = -98 \][/tex]
### Step 3: Divide the result by 7
[tex]\[ -98 \div 7 = -14 \][/tex]
### Step 4: Add [tex]\( 12 \)[/tex] and [tex]\( b \)[/tex] to the result
Given [tex]\( b = 1 \)[/tex],
[tex]\[ 12 + (-14) + 1 = -1 \][/tex]
So, the final result of the expression when [tex]\( a = 5 \)[/tex] and [tex]\( b = 1 \)[/tex] is
[tex]\[ -1 \][/tex]
Now, let's plot this result on the provided number line:
```
<---------------------------|--------------------------->
-10 0 10
```
Marking [tex]\(-1\)[/tex] on the number line:
```
<------|---------------------|---------------------------|-->
-10 -5 0
```
A point should be placed just one tick mark to the left of zero, indicating [tex]\(-1\)[/tex].
