https://file.aiquickdraw.com/mathbot/file/1726766245520y0l3ua7z.jpg

Let's go through the math problems shown in the image and work on solving them step by step.

### 5. Finding the length of segment \( AD \):

We are given the following:
- \( AC = 18 \, \text{cm} \)
- \( BD = 20 \, \text{cm} \)
- \( BC = 6 \, \text{cm} \)

Since \( BD = BC + CD \), we find \( CD = BD - BC = 20 \, \text{cm} - 6 \, \text{cm} = 14 \, \text{cm} \).

Now, \( AD = AC + CD = 18 \, \text{cm} + 14 \, \text{cm} = 32 \, \text{cm} \).

The correct answer is **B) 32 cm**.

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### 6. Identifying the point that does not belong to ray \( BD \):

In the diagram, the ray starts at \( B \) and passes through \( D \), extending to the right. Points on the ray must be located on this path. By observation:
- \( M, B, D, E \) are aligned on the ray.
- \( K \) is located to the left of \( B \), and hence does not lie on the ray.

The correct answer is **Г) K**.

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### 7. Finding the coordinate of point \( M \):

From the number line provided, we can observe that the number 6 is assigned to point \( M \). The coordinates are equally spaced, confirming this.

The correct answer is **Б) 6**.

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### 8. Finding the coordinate of point \( K \):

On the number line, the coordinates increase in increments of 15. From \( 0 \), moving five spaces brings us to \( 75 \), which corresponds to point \( K \).

The correct answer is **Г) 75**.

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### 9. Solving the inequality \( 1472 > 14*4 \):

We need to replace the \( * \) in \( 14*4 \) with a number so that the inequality holds true. Calculating:
- \( 1472 \) is already given.
- \( 14 \times 4 = 56 \), so \( 14*4 \) should be less than 1472.
  
Substituting different options:
- If \( * = 8 \), we get \( 14 \times 8 = 112 \), which makes \( 1472 > 112 \), and the inequality holds.

The correct answer is **А) 8**.

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Do you want more detailed steps on any of these solutions?

### 5 Related Questions:
1. How do you approach ray problems geometrically?
2. What is the significance of the point positions on a number line?
3. How can you verify the length of a segment when multiple segments are involved?
4. What is the process for solving inequalities with unknown variables?
5. How does one read and interpret a number line?

#### Tip:
Always double-check the alignment of points on a diagram, as visual placement can help identify key relationships between segments and rays.

Several math problems from a textbook focusing on geometry, number lines, and inequalities.

Solve geometry problems involving segment lengths and number lines, along with inequality challenges. This lesson includes detailed steps for calculating segment lengths, identifying points on a number line, and solving inequalities for students in Grades 5-7.

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