https://file.aiquickdraw.com/mathbot/file/172822507760963i4s7e8.jpg

Let's break down the problems in the image.

### Question 8:
It involves a rectangle $ PQRS $, and the lengths of $ PM $ and $ QM $ are given as:
- $ PM = 6x - 8 $
- $ QM = 2x + 4 $

We need to find the value of $ x $. Since $ M $ is the midpoint of $ PQ $ and $ PR $, the lengths of $ PM $ and $ QM $ are equal:
\[
6x - 8 = 2x + 4
\]
Solve for $ x $:
\[
6x - 2x = 4 + 8 \\
4x = 12 \\
x = 3
\]
Thus, the value of $ x $ is 3.

### Question 9:
This question asks about choosing one inside sports activity and one outside sports activity. The possible combinations come from:
- Inside: **Basketball**, **Table Tennis**
- Outside: **Cricket**, **Football**

So, the possible combinations are:
\[
2 \times 2 = 4 \, \text{combinations}
\]
Thus, the answer is 4.

### Question 11:
The total cost of a device includes material, labor, and general costs in the ratio of 1:4:3. If the material cost is \$315, we need to find the total cost.
The total cost is calculated using the ratio's sum:
\[
1 + 4 + 3 = 8
\]
The material cost corresponds to the "1" part in the ratio, so the total cost is:
\[
\text{Total Cost} = 315 \times 8 = 2520 \, \text{dollars}
\]
Thus, the total cost is \$2520.

### Question 12:
The given numbers are 3.2, 3.154, 3.0007, and 3.00125. The largest number is **3.2**.

### Question 13:
The area of the board is $ 0.3 \, \text{m}^2 $, and we need to convert this to $ \text{cm}^2 $. Since 1 $ \text{m}^2 = 10,000 \, \text{cm}^2 $:
\[
0.3 \, \text{m}^2 = 0.3 \times 10,000 = 3000 \, \text{cm}^2
\]
Thus, the area is 3000 cm².

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Would you like further details on any of these answers? Here are five related questions you could explore:

1. What are the properties of a rectangle and its diagonals?
2. How do you solve linear equations with variables on both sides?
3. Can you calculate other costs using ratios?
4. How are decimal numbers compared accurately?
5. How do you convert between different units of area?

### Tip:
Always double-check your calculations when dealing with unit conversions, as small mistakes can lead to incorrect answers.

This image contains several math-related problems, focusing on algebra, ratios, unit conversions, and comparisons of numbers.

This page covers a variety of math problems for Grade 8-9 students, including solving linear equations, calculating combinations, working with ratios, comparing decimals, and converting units of area. Detailed solutions are provided for each problem.

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