Question

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{\frac{2 x}{3}+5} ; 6$$

Short answer

The result of evaluating the function for \(x = 6\) and rounding to the nearest tenth is \(y = 3.0\)

Step-by-step solution

Substituting the Value of x

Substitute \(x = 6\) into the function \(y= \sqrt{\frac{2x}{3}+5}\). This gives: \(y = \sqrt{\frac{2(6)}{3} + 5}\)

Simplify the Fraction in the Square Root

Simplify the fraction to get: \(y = \sqrt{4 + 5} = \sqrt{9}\)

Calculate the Square Root

Calculate the square root: \(y = 3\)

Round to the Nearest Tenth

Since there are no decimal points in the answer, rounding 3 to the nearest tenth gives: \(y = 3.0\)