Questions: Evaluate the expression when (x=4) and (y=2). ((4 y+x^2)/y) Simplify your answer as much as possible.

Transcript text: Evaluate the expression when $x=4$ and $y=2$. \[ \frac{4 y+x^{2}}{y} \] Simplify your answer as much as possible.

Solution

Step 1: Substitute the values of $ x $ and $ y $

Given the expression: \[ \frac{4y + x^{2}}{y} \]

We need to evaluate it when $ x = 4 $ and $ y = 2 $. Substitute these values into the expression: \[ \frac{4(2) + 4^{2}}{2} \]

Step 2: Simplify the numerator

Calculate the values inside the numerator: \[ 4(2) = 8 \] \[ 4^{2} = 16 \] So the numerator becomes: \[ 8 + 16 = 24 \]

Step 3: Divide by the denominator

Now, divide the simplified numerator by the denominator: \[ \frac{24}{2} = 12 \]

$\boxed{12}$

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