Sure, let's evaluate the expression [tex]\((-3.8) + 2 + y\)[/tex] for the given values of [tex]\( y \)[/tex].
1. For [tex]\( y = -2 \)[/tex]:
Substitute [tex]\( y = -2 \)[/tex] into the expression:
[tex]\[
(-3.8) + 2 + (-2) = -3.8 + 2 - 2 = -3.8 + 0 = -3.8
\][/tex]
So, the value of the expression for [tex]\( y = -2 \)[/tex] is [tex]\(-3.8\)[/tex].
2. For [tex]\( y = 1.8 \)[/tex]:
Substitute [tex]\( y = 1.8 \)[/tex] into the expression:
[tex]\[
(-3.8) + 2 + 1.8 = -3.8 + 2 + 1.8 = -3.8 + 3.8 \approx 2.220446049250313e-16
\][/tex]
So, the value of the expression for [tex]\( y = 1.8 \)[/tex] is approximately [tex]\( 2.220446049250313e-16 \)[/tex]. This is a very small number close to zero, which occurs due to floating-point arithmetic precision limits.
3. For [tex]\( y = 0 \)[/tex]:
Substitute [tex]\( y = 0 \)[/tex] into the expression:
[tex]\[
(-3.8) + 2 + 0 = -3.8 + 2 = -1.8
\][/tex]
So, the value of the expression for [tex]\( y = 0 \)[/tex] is approximately [tex]\(-1.7999999999999998\)[/tex], which is very close to [tex]\(-1.8\)[/tex].
4. For [tex]\( y = 3.8 \)[/tex]:
Substitute [tex]\( y = 3.8 \)[/tex] into the expression:
[tex]\[
(-3.8) + 2 + 3.8 = -3.8 + 2 + 3.8 = -3.8 + 3.8 + 2 = 2.0
\][/tex]
So, the value of the expression for [tex]\( y = 3.8 \)[/tex] is [tex]\( 2.0 \)[/tex].
The completed table is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{y} & \text{Value of expression} \\
\hline
-2 & -3.8 \\
\hline
1.8 & 2.220446049250313e-16 \\
\hline
0 & -1.7999999999999998 \\
\hline
3.8 & 2.0 \\
\hline
\end{tabular}
\][/tex]
