High School

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Use the function to answer the question.

[tex]\[ F(t) = 212 - 6t \][/tex]

What is the value of [tex]\( t \)[/tex] when [tex]\( F(t) = 140 \)[/tex]?

A. -840
B. -628
C. 12
D. 66
E. 72

Answer :

To determine the value of [tex]\( t \)[/tex] when [tex]\( F(t) = 140 \)[/tex], we start with the given function:

[tex]\[ F(t) = 212 - 6t \][/tex]

We need to find [tex]\( t \)[/tex] such that:

[tex]\[ 212 - 6t = 140 \][/tex]

1. First, isolate the term involving [tex]\( t \)[/tex]. Subtract 140 from both sides of the equation:

[tex]\[ 212 - 140 = 6t \][/tex]
[tex]\[ 72 = 6t \][/tex]

2. Now, solve for [tex]\( t \)[/tex] by dividing both sides by 6:

[tex]\[ t = \frac{72}{6} \][/tex]
[tex]\[ t = 12 \][/tex]

Thus, the value of [tex]\( t \)[/tex] when [tex]\( F(t) = 140 \)[/tex] is:

[tex]\[ t = 12 \][/tex]

The correct answer is:
C. 12

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