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The image contains a math exam or worksheet labeled "Trabajo Práctico Integrador" from "Prof. Arro," with various mathematical problems. Here’s a breakdown of the content:

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**1. Ejercicios Combinados (Combined Exercises):**

a)  
\[
\frac{3}{2} \cdot \left( \frac{\sqrt{25}}{4} \right)^{-2} + \frac{2}{3} - \left( 1 - \frac{3}{4} + \sqrt{\frac{5}{32}} \right)^{-1}
\]

b)  
\[
\left( \frac{5}{2} \right)^{-1} \cdot \left( \frac{\sqrt{22}}{25} \right)^{-2} - \frac{63}{81}
\]

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**2. Ecuaciones (Equations):**

a)  
\[
7 \cdot (x - 5) - x = 3
\]

b)  
\[
4x + 7 \cdot (2x - 5) = (x - 3) = (8 - x)
\]

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**3. Sistemas (Systems of Equations):**  
Resolver por igualar o métodos analíticos (Solve by equalizing or using analytical methods).

\[
\begin{aligned}
1) & \quad x + 5y = 5 \\
   & \quad 3x - 5y = 3
\end{aligned}
\]

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**4. Optimizar las siguientes funciones (Optimize the following functions):**

a)  
\[
f(x) = -2x + 3
\]

b)  
\[
f(x) = -x^2 + 4x - 3
\]

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**5. Resolver con Teorema de Pitágoras y razones trigonométricas (Solve using Pythagoras' Theorem and trigonometric ratios):**

Two right triangles:

A) One with legs of 15 and 8.  
B) One with legs of 20 and 5.

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Would you like me to solve any of these specific exercises? Feel free to select one or more, and I can guide you through the solution.

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### Related Questions:
1. How do you simplify expressions involving roots and powers?
2. What methods are used to solve linear equations like those in part 2?
3. How do you solve a system of linear equations using the elimination method?
4. What is the process for optimizing a quadratic function?
5. How are trigonometric ratios applied in solving right triangles?

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### Tip:
When optimizing quadratic functions, always remember that the vertex provides the maximum or minimum value depending on the parabola's orientation (concave up or down).

Math exam or worksheet labeled 'Trabajo Práctico Integrador' by Prof. Arro with combined exercises, equations, systems of equations, optimization, and Pythagorean Theorem problems.

Solve a variety of math problems covering combined algebraic exercises, systems of linear equations, function optimization, and geometry with the Pythagorean Theorem. Suitable for students in Grades 9-12.

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