To find the output, [tex]\( k \)[/tex], when the input, [tex]\( t \)[/tex], is [tex]\(-7\)[/tex], we use the formula given:
[tex]\[
k = 10t - 19
\][/tex]
Now, let's substitute the value of [tex]\( t \)[/tex] into the equation.
Given: [tex]\( t = -7 \)[/tex]
Substitute [tex]\( t \)[/tex] in the formula:
[tex]\[
k = 10(-7) - 19
\][/tex]
So, we multiply [tex]\( 10 \)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
10 \times (-7) = -70
\][/tex]
Next, we subtract [tex]\( 19 \)[/tex] from [tex]\(-70\)[/tex]:
[tex]\[
-70 - 19 = -89
\][/tex]
Therefore, the output [tex]\( k \)[/tex] when [tex]\( t \)[/tex] is [tex]\(-7\)[/tex] is:
[tex]\[
k = -89
\][/tex]
