Let's solve each problem step by step from the uploaded image.

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9. Solve the equation $2x - 3 = 5$ and represent the solution on the given number line.

1. Solve for $x$: $2x - 3 = 5 \quad \implies \quad 2x = 8 \quad \implies \quad x = 4$

2. Representation on the number line: Mark $x = 4$ on the number line.

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10. How many cube-shaped pieces of metal (2 cm on each side) can be added to the cylinder without overflowing the water?

• Cylinder information:

  • Height of the cylinder = 20 cm
  • Initial height of water = 10 cm
  • Volume of the cylinder = $\pi r^2 h$

• Volume of water in the cylinder: $\text{Volume of water} = \pi r^2 \cdot 10 \quad (\text{since initial height is 10 cm})$

• Remaining volume before overflow: $\text{Remaining volume} = \pi r^2 (20 - 10) = \pi r^2 \cdot 10$

• Volume of each cube: $\text{Volume of one cube} = 2^3 = 8 \, \text{cm}^3$

Divide the remaining volume by 8 to find how many cubes fit. Assuming $r^2$ and cylinder volume are given.

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11. Find the length of $OX$:

Given:

• $CD = 12 \, \text{cm}$
• $OY = 3 \, \text{cm}$
• $DX = 2 \, \text{cm}$

From the circle properties and right triangles: $OX^2 = OY^2 + DX^2$ Substitute: $OX^2 = 3^2 + 2^2 = 9 + 4 = 13$ $OX = \sqrt{13} \, \text{cm}$

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12. Find the value of $\sqrt{26}$ to the first contraction.

The square root of $26$ is approximately: $\sqrt{26} \approx 5.1$

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13. Pair of congruent triangles in the parallelogram:

From the diagram, the pair of congruent triangles is: $\triangle APB \cong \triangle CPD$ Reason: $AP \parallel CD$ and $AB = CD$ (properties of parallelogram).

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14. Find the least common multiple of $5x^3, 10xy, 2xy^2$:

1. Factorize:

   • $5x^3 = 5 \cdot x^3$
   • $10xy = 2 \cdot 5 \cdot x \cdot y$
   • $2xy^2 = 2 \cdot x \cdot y^2$

2. LCM: Take the highest powers of all factors: $\text{LCM} = 2 \cdot 5 \cdot x^3 \cdot y^2 = 10x^3y^2$

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Let me know which steps need further explanation or details! Here are some related questions:

1. Can you explain how the solution for $x$ in problem 9 is represented graphically?
2. Would you like a detailed calculation for the remaining volume in problem 10?
3. Do you need a visual explanation of congruent triangles in problem 13?
4. Would you like help understanding the LCM calculation in problem 14?
5. Do you need further steps for estimating $\sqrt{26}$ more precisely?

Tip: For geometry problems, always sketch the diagram and label known values for clarity!