Question
\( \frac{3 x^{2}+y}{2}=z-\frac{y}{4} \) Given \( x=2 \) and \( y=8 \), solve for \( z \)
Ask by Weaver Hilton. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z = 12 \)
Solution
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 \( 12 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To solve for \( z \), we start by substituting the values of \( x \) and \( y \) into the equation: \[ \frac{3(2)^{2}+8}{2}=z-\frac{8}{4} \] Now calculate \( 3(2)^{2} + 8 \): \[ 3(4) + 8 = 12 + 8 = 20 \] So the equation becomes: \[ \frac{20}{2} = z - 2 \] This simplifies to: \[ 10 = z - 2 \] Now, add 2 to both sides to isolate \( z \): \[ z = 10 + 2 = 12 \] Thus, the value of \( z \) is \( 12 \).
