To determine the value of [tex]\( y \)[/tex], given [tex]\( x = 5 \)[/tex] and the equation [tex]\( y = \frac{38}{x + 14} \)[/tex], we will follow these steps:
1. Substitute the value of [tex]\( x \)[/tex] into the equation:
Given [tex]\( x = 5 \)[/tex], we replace [tex]\( x \)[/tex] in the equation with 5. The equation becomes:
[tex]\[
y = \frac{38}{5 + 14}
\][/tex]
2. Simplify the expression in the denominator:
Calculate the sum inside the denominator:
[tex]\[
5 + 14 = 19
\][/tex]
3. Substitute this sum back into the equation:
Now, the equation is:
[tex]\[
y = \frac{38}{19}
\][/tex]
4. Perform the division:
Divide 38 by 19:
[tex]\[
y = 2
\][/tex]
Thus, the value of [tex]\( y \)[/tex] is [tex]\( 2.0 \)[/tex].
