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The image contains three math problems. I'll solve each one and provide the answers with explanations.

### Problem 1:
\[
2(2x + 3) = 4x + 8
\]
We are asked to find the value of \( x \) that satisfies this equation.

**Solution:**
1. Distribute the \( 2 \) on the left side:
   \[
   4x + 6 = 4x + 8
   \]
2. Subtract \( 4x \) from both sides:
   \[
   6 = 8
   \]
   This is a contradiction, which means the equation has **no solution**.

### Problem 2:
This problem involves analyzing a graph and solving based on its features. The graph represents a parabola.

**Problem Statement:**
Determine the range of \( x \) where the height \( y \) of the projectile is at least 8 meters.

**Solution:**
- The graph shows a parabola with its vertex at \( x = 3 \) and \( y = 10 \) meters.
- The height of 8 meters corresponds to points where the parabola crosses \( y = 8 \).

By analyzing the graph:
- The parabola crosses \( y = 8 \) at approximately \( x = 2 \) and \( x = 4 \).
- Thus, the range of \( x \) where the height is at least 8 meters is \( 2 \leq x \leq 4 \).

### Problem 3:
**Problem Statement:**
Two poles, A and B, are located 60 meters apart. The height of pole A is 20 meters, and the height of pole B is 40 meters. A rope is tied from the top of pole A to the top of pole B. What is the height of the rope when it is at a point directly above the point on the ground that is 30 meters from both poles?

**Solution:**
This is a classic application of similar triangles.

Let's denote the height of the rope above the ground at the midpoint between the two poles as \( h \). The midpoint is 30 meters from each pole.

1. Since the point is equidistant from both poles:
   \[
   \text{Using the similarity of triangles: } \frac{h}{30} = \frac{40 - 20}{60}
   \]
2. Simplifying:
   \[
   \frac{h}{30} = \frac{20}{60} = \frac{1}{3}
   \]
   So, \( h = 10 \) meters.

Thus, the height of the rope at that point is **10 meters**.

---

If you need further details on any of these solutions or have any questions, feel free to ask!

### Relative Questions:
1. How do you determine when a quadratic equation has no solution?
2. What are the properties of a parabola that help in solving graph-based questions?
3. How do you apply the concept of similar triangles in real-life problems?
4. What is the significance of the vertex in a parabolic graph?
5. How do you solve linear equations with variables on both sides?
6. What is the range and how is it determined in the context of a graph?
7. How can contradictions in algebraic equations be identified?
8. How can you find the point where a rope is at its lowest height between two poles?

### Tip:
Always check for contradictions when solving equations; if both sides simplify to a false statement, the equation has no solution.

Explore how to solve quadratic equations, analyze graphs of parabolas, and apply similar triangles in real-life problems. Includes step-by-step solutions and explanations. Suitable for high school students.

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