To find the value of [tex]\( y \)[/tex] when [tex]\( x = \frac{4}{5} \)[/tex], we will substitute [tex]\( x \)[/tex] into the given formula [tex]\( y = \frac{4}{x} + \sqrt{x + 0.2} - 5x \)[/tex].
1. Start with the formula:
[tex]\[
y = \frac{4}{x} + \sqrt{x + 0.2} - 5x
\][/tex]
2. Substitute [tex]\( x = \frac{4}{5} \)[/tex] into the formula:
[tex]\[
y = \frac{4}{\frac{4}{5}} + \sqrt{\frac{4}{5} + 0.2} - 5 \left( \frac{4}{5} \right)
\][/tex]
3. Simplify the fraction:
[tex]\[
\frac{4}{\frac{4}{5}} = 4 \cdot \frac{5}{4} = 5
\][/tex]
4. Add the fractions inside the square root:
[tex]\[
\frac{4}{5} + 0.2 = \frac{4}{5} + \frac{1}{5} = \frac{5}{5} = 1
\][/tex]
5. Calculate the square root:
[tex]\[
\sqrt{1} = 1
\][/tex]
6. Multiply and simplify the final term:
[tex]\[
5 \left( \frac{4}{5} \right) = 4
\][/tex]
7. Plug all these simplified parts back into the equation:
[tex]\[
y = 5 + 1 - 4
\][/tex]
8. Perform the arithmetic operation to find [tex]\( y \)[/tex]:
[tex]\[
y = 5 + 1 - 4 = 2
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
