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The problem you've provided asks about two equations:

\[
m = \frac{7}{2} p^2 + 9
\]
\[
n = \frac{5}{2} p^2 + 4
\]

We need to analyze the relationship between \( m \), \( n \), and \( p \), based on the multiple-choice options provided:

A. \( m > n \)  
B. \( m < n \)  
C. \( m - p = n \)  
D. \( p = n + m \)

### Let's start by subtracting the equation for \( n \) from the equation for \( m \):

\[
m - n = \left(\frac{7}{2} p^2 + 9\right) - \left(\frac{5}{2} p^2 + 4\right)
\]
Simplifying the right-hand side:

\[
m - n = \frac{7}{2} p^2 + 9 - \left(\frac{5}{2} p^2 + 4\right)
\]
\[
m - n = \left(\frac{7}{2} - \frac{5}{2}\right) p^2 + (9 - 4)
\]
\[
m - n = \frac{2}{2} p^2 + 5
\]
\[
m - n = p^2 + 5
\]

From this equation, we can observe that \( m \) is always greater than \( n \) because \( p^2 \) is non-negative (for all real values of \( p \)) and we are adding 5 to it.

Thus, the correct answer is:
**A. \( m > n \)**.

Would you like more details, or do you have any questions?

Here are 5 additional questions related to the problem:
1. How does the value of \( p \) affect the difference between \( m \) and \( n \)?
2. What would happen to the relationship between \( m \) and \( n \) if the constants were different?
3. Can we find specific values of \( p \) where \( m - n = 10 \)?
4. How would the inequality change if we swapped the coefficients in the equations for \( m \) and \( n \)?
5. Can this method of comparing \( m \) and \( n \) be used for any quadratic equation?

**Tip:** Always simplify both sides of an equation before comparing terms—it helps in identifying relationships more clearly!

Jika m = (7/2)p^2 + 9. Dan n = (5/2)p^2 + 4. Maka ...

Solve the comparison between two quadratic equations: m = (7/2)p^2 + 9 and n = (5/2)p^2 + 4. Learn how to find the relationship between m, n, and p, with step-by-step algebraic solutions suitable for Grades 9-10.

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