I.` (x-18)^(2) = 0" "II. Y^(2)=324`

Options

A. if `x gt y`
B. if `x ge y`
C. if ` y gt x `
D. if ` y ge x`

Explanation

To solve the equations provided, we will go through each equation step by step.

### Step 1: Solve the first equation
The first equation is:
\[ (x - 18)^2 = 0 \]
To solve for \(x\), we take the square root of both sides:
\[ x - 18 = 0 \]
Now, we add 18 to both sides:
\[ x = 18 \]

### Step 2: Solve the second equation
The second equation is:
\[ y^2 = 324 \]
To solve for \(y\), we take the square root of both sides:
\[ y = \pm \sqrt{324} \]
Calculating the square root:
\[ y = \pm 18 \]
This means:
\[ y = 18 \quad \text{or} \quad y = -18 \]

### Step 3: Determine the relationship between \(x\) and \(y\)
Now we have the values:
- \(x = 18\)
- \(y = 18\) or \(y = -18\)

We can compare \(x\) and \(y\):
1. When \(y = 18\), \(x = y\).
2. When \(y = -18\), \(x > y\).

Thus, we can conclude that:
\[ x \geq y \]

### Final Conclusion
The relationship between \(x\) and \(y\) is:
\[ x \geq y \]