Let's evaluate the given expression step-by-step:
Given the expression:
[tex]\[ 12 + \left[2 - \left(4 \cdot a^2\right)\right] \div 7 + b \][/tex]
1. Substitute the given values:
[tex]\[ a = 5 \][/tex]
[tex]\[ b = 1 \][/tex]
2. Calculate [tex]\( 4 \cdot a^2 \)[/tex]:
[tex]\[ 4 \cdot 5^2 = 4 \cdot 25 = 100 \][/tex]
3. Subtract the result from 2:
[tex]\[ 2 - 100 = -98 \][/tex]
4. Divide this result by 7:
[tex]\[ -98 \div 7 = -14 \][/tex]
5. Add 12 to this quotient:
[tex]\[ 12 + (-14) = -2 \][/tex]
6. Finally, add [tex]\( b \)[/tex]:
[tex]\[ -2 + 1 = -1 \][/tex]
So, the resulting value is [tex]\(-1\)[/tex].
To plot this value on a number line, locate the point [tex]\(-1\)[/tex] and mark it accordingly.
