Let's evaluate and match each expression on the left to its value on the right when [tex]\( x = 7 \)[/tex] and [tex]\( y = 4 \)[/tex].
Here are the expressions to evaluate:
1. [tex]\( 12 + x \)[/tex]
2. [tex]\( 3x + y \)[/tex]
3. [tex]\( 4y - 10 \)[/tex]
4. [tex]\( \frac{1}{2}xy \)[/tex]
### Step-by-Step Evaluation:
1. Evaluate [tex]\( 12 + x \)[/tex] when [tex]\( x = 7 \)[/tex]:
[tex]\[
12 + x = 12 + 7 = 19
\][/tex]
So, [tex]\( 12 + x \)[/tex] equals 19.
2. Evaluate [tex]\( 3x + y \)[/tex] when [tex]\( x = 7 \)[/tex] and [tex]\( y = 4 \)[/tex]:
[tex]\[
3x + y = 3 \times 7 + 4 = 21 + 4 = 25
\][/tex]
So, [tex]\( 3x + y \)[/tex] equals 25.
3. Evaluate [tex]\( 4y - 10 \)[/tex] when [tex]\( y = 4 \)[/tex]:
[tex]\[
4y - 10 = 4 \times 4 - 10 = 16 - 10 = 6
\][/tex]
So, [tex]\( 4y - 10 \)[/tex] equals 6.
4. Evaluate [tex]\( \frac{1}{2}xy \)[/tex] when [tex]\( x = 7 \)[/tex] and [tex]\( y = 4 \)[/tex]:
[tex]\[
\frac{1}{2}xy = \frac{1}{2} \times 7 \times 4 = 3.5 \times 4 = 14
\][/tex]
So, [tex]\( \frac{1}{2}xy \)[/tex] equals 14.
### Matching:
Now let's match these evaluated values with the given answers on the right:
- [tex]\( 12 + x \)[/tex] which is 19
- [tex]\( 3x + y \)[/tex] which is 25
- [tex]\( 4y - 10 \)[/tex] which is 6
- [tex]\( \frac{1}{2}xy \)[/tex] which is 14
Therefore, the correct matching is:
[tex]\[
\begin{tabular}{ll}
$12 + x$ & 19 \\
$3x + y$ & 25 \\
$4y - 10$ & 6 \\
$\frac{1}{2}xy$ & 14 \\
\end{tabular}
\][/tex]
These are the correct matches for the expressions with their values.
