https://r2.erweima.ai/mathbot/image/1726721410607j5n46kj7.jpg

The image you uploaded contains mathematical exercises written in Persian (Farsi) and includes geometric figures. To assist you better, I will extract and explain the contents. Here is what I can interpret so far from the image:

1. **First Problem (Top Left Section)**: 
   - It seems to be a problem involving probability. You are asked to find the probability of event \( P(A \cap B) = P(A \text{ and } B) \).
   - Further details include finding \( P(A | B) \) and related probabilities.

2. **Second Problem (Middle Left Section)**:
   - It involves geometry, where the task is to calculate the height of a given triangle or some geometrical figure. The square root term \( \sqrt{...} \) indicates possibly using the Pythagorean theorem or other methods to find lengths.

3. **Third Problem (Bottom Left Section)**:
   - The problem seems to involve systems of equations or some algebraic expressions. The equation \( x + mt = k^3 + t \) could be related to solving for specific values of \( x \) and \( t \).

4. **Right Side Geometry Problems (Geometric Shapes)**:
   - Two triangles \( ABC \) and \( AEF \) are shown.
   - The task seems to ask about the similarity or congruence of these triangles, possibly proving them using geometric properties.

   - Further, there's a possible requirement to calculate sides or angles in terms of the given variables.

### To help you solve these problems:
1. Do you need a step-by-step solution for one of the specific problems, or would you prefer an overview of all of them?
2. Let me know if you would like any part of the problem translated in more detail, or if you want a deeper explanation of certain terms.

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Here are 5 relative questions to expand on:
1. Would you like help solving the probability problem in the first section?
2. Should I walk you through the geometric properties of the triangles shown?
3. Do you need assistance with any of the algebraic equations present in the image?
4. Should I explain how to calculate the height of a triangle using the square root expression?
5. Would you like help translating more of the Persian text for clarity?

**Tip**: When dealing with geometric problems, try breaking them down into known shapes (like triangles or rectangles) and use properties like the Pythagorean theorem or trigonometric identities to simplify calculations.

Mathematical problems involving probability, geometry, and algebra from an image written in Persian. It includes calculating probabilities, solving for variables in equations, and analyzing geometric properties of triangles.

This page provides step-by-step solutions to mathematical problems in probability, algebra, and geometry, including finding probabilities, solving for variables, and analyzing triangle properties. Suitable for Grades 9-11.

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