$$ \frac{3 x^{2}+y}{2}=z-\frac{y}{4} $$ Given $$ x=2 $$ and $$ y=8 $$, solve for $$ z $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   \frac{3x^2 + y}{2} = z - \frac{y}{4}
   $$

2. Substitute $$ x = 2 $$ and $$ y = 8 $$ into the equation:
   $$
   \frac{3(2)^2 + 8}{2} = z - \frac{8}{4}
   $$

3. Calculate $$ 3(2)^2 $$:
   $$
   3(4) = 12
   $$

4. Replace the value in the numerator:
   $$
   \frac{12 + 8}{2} = z - \frac{8}{4}
   $$

5. Simplify the numerator:
   $$
   \frac{20}{2} = z - 2
   $$

6. Divide $$ 20 $$ by $$ 2 $$:
   $$
   10 = z - 2
   $$

7. Solve for $$ z $$ by adding $$ 2 $$ to both sides:
   $$
   z = 10 + 2 = 12
   $$

Thus, the value of $$ z $$ is $$ 12 $$.
$$ z = 12 $$

\( \frac{3 x^{2}+y}{2}=z-\frac{y}{4} \) Given \( x=2 \) and \( y=8 \), solve for \( z \)