Sure, let's evaluate the given expression step-by-step when [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex].
The expression to evaluate is:
[tex]\[
\frac{4y + x^2}{y}
\][/tex]
1. Substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- [tex]\( x = 4 \)[/tex]
- [tex]\( y = 2 \)[/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the expression:
[tex]\[
\frac{4(2) + 4^2}{2}
\][/tex]
2. Calculate [tex]\( 4y \)[/tex] and [tex]\( x^2 \)[/tex]:
- [tex]\( 4y = 4 \cdot 2 = 8 \)[/tex]
- [tex]\( x^2 = 4^2 = 16 \)[/tex]
Now the expression looks like:
[tex]\[
\frac{8 + 16}{2}
\][/tex]
3. Add the terms in the numerator:
[tex]\[
8 + 16 = 24
\][/tex]
So the expression now becomes:
[tex]\[
\frac{24}{2}
\][/tex]
4. Divide the numerator by the denominator:
[tex]\[
\frac{24}{2} = 12
\][/tex]
So, the value of the expression when [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex] is:
[tex]\[
12.0
\][/tex]
