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It looks like you've uploaded an image containing a mathematics exam or worksheet, focusing on geometry, algebra, and trigonometry. Here’s an outline of some of the questions that I can help you with:

1. **Question 26**: Proving that \(2 - \frac{\sqrt{3}}{5}\) is an irrational number, assuming that \(\sqrt{3}\) is irrational.
2. **Question 27**: Finding the dimensions of a rectangular garden, given that the half-perimeter is 36 meters and the length is 4 meters more than the width.
3. **Question 28**: Proving that \(a^2 + b^2 = m^2 + n^2\), given two trigonometric equations.
4. **Question 29**: Finding the ratio in which a line divides a line segment and determining the point of intersection of two lines.
5. **Question 30**: Proving that \(\frac{AB}{PQ} = \frac{AD}{PM}\), where \( \triangle ABC \sim \triangle PQR \).
6. **Question 31**: Proving that a parallelogram circumscribing a circle is a rhombus.

Let me know if you'd like me to work on the solution to any of these specific problems!

Find the ratio in which the lines x - 3y = 0 divide the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection.

This problem asks to find the ratio in which the line x - 3y = 0 divides the line segment joining points (-2, -5) and (6, 3), and calculate the coordinates of their intersection. Suitable for students in Grades 10-12, focusing on coordinate geometry and section formula.

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