Let's break down the expression and determine its value when [tex]\( t = -12 \)[/tex].
The expression given is:
[tex]\[ -3 |t - 8| + 1.5 \][/tex]
First, substitute [tex]\( t = -12 \)[/tex] into the expression:
[tex]\[ -3 |-12 - 8| + 1.5 \][/tex]
Calculate inside the absolute value:
[tex]\[ t - 8 = -12 - 8 = -20 \][/tex]
The absolute value of [tex]\(-20\)[/tex] is:
[tex]\[ |-20| = 20 \][/tex]
Next, multiply this by [tex]\(-3\)[/tex]:
[tex]\[ -3 \times 20 = -60 \][/tex]
Finally, add 1.5 to the result:
[tex]\[ -60 + 1.5 = -58.5 \][/tex]
So, the value of the expression when [tex]\( t = -12 \)[/tex] is [tex]\(-58.5\)[/tex].
Thus, the correct answer is:
D. -58.5
