**Understanding Repeating Patterns**Consider a recurring pattern. Assume it continuously repeats. The aim is to find the total number of plus signs in the pattern from shape 1 through shape 400.**The Pattern:**1. Plus sign (green cross)2. Diamond (purple diamond)3. Star (orange star)4. Star (orange star)5. Heart (red heart)6. Heart (red heart)This sequence repeats every 6 steps.**Diagram:**- Shape 1: Green Plus- Shape 2: Purple Diamond- Shape 3: Orange Star- Shape 4: Orange Star- Shape 5: Red Heart- Shape 6: Red Heart- Shape 7: Green Plus- Shape 8: Purple Diamond- Shape 9: Orange Star- Shape 10: Orange Star- Shape 11: Red Heart- Shape 12: Red Heart- Shape 13: Green Plus- Shape 14: Purple Diamond- Shape 15: Orange Star- Shape 16: Orange Star- Shape 17: Red Heart- Shape 18: Red Heart- Shape 19: Green Plus- Shape 20: Purple Diamond (continuing...)- Shape 21: Orange Star- Shape 22: Orange Star- Shape 23: Red Heart- Shape 24: Purple Diamond**Finding the Total Number of Plus Signs from Shape 1 to Shape 400:**1. **Identify the Repeating Cycle:** - Each cycle of 6 shapes contains 1 Green Plus.2. **Determine How Many Complete Cycles Fit into 400 Shapes:** - \( \frac{400}{6} = 66 \text{ complete cycles} \) with a remainder of 4 shapes.3. **Calculate the Number of Plus Signs in these Cycles:** - In each complete cycle, there is 1 plus sign. - Number of plus signs in 66 cycles: \( 66 \times 1 = 66 \)4. **Consider the Remaining Shapes (after 66 Full Cycles):** - Remaining shapes: 4 (after 396 shapes, 4 more shapes are considered) - Check these remaining shapes: Green Plus, Purple Diamond, Orange Star, Orange Star (1 plus sign from these 4 shapes)5. **

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Consider that same repeating pattern. Assume it continues to repeat. Find the total number of plus signs in the pattern from shape 1 through shape 400. 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Consider that same repeating pattern. Assume it continues to repeat. Find the total number of plus signs in the pattern from shape 1 through shape 400. 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Understanding Repeating Patterns**

Consider a recurring pattern. Assume it continuously repeats. The aim is to find the total number of plus signs in the pattern from shape 1 through shape 400.

**The Pattern:**
1. Plus sign (green cross)
2. Diamond (purple diamond)
3. Star (orange star)
4. Star (orange star)
5. Heart (red heart)
6. Heart (red heart)

This sequence repeats every 6 steps.

**Diagram:**
- Shape 1: Green Plus
- Shape 2: Purple Diamond
- Shape 3: Orange Star
- Shape 4: Orange Star
- Shape 5: Red Heart
- Shape 6: Red Heart
- Shape 7: Green Plus
- Shape 8: Purple Diamond
- Shape 9: Orange Star
- Shape 10: Orange Star
- Shape 11: Red Heart
- Shape 12: Red Heart
- Shape 13: Green Plus
- Shape 14: Purple Diamond
- Shape 15: Orange Star
- Shape 16: Orange Star
- Shape 17: Red Heart
- Shape 18: Red Heart
- Shape 19: Green Plus
- Shape 20: Purple Diamond (continuing...)
- Shape 21: Orange Star
- Shape 22: Orange Star
- Shape 23: Red Heart
- Shape 24: Purple Diamond

**Finding the Total Number of Plus Signs from Shape 1 to Shape 400:**

1. **Identify the Repeating Cycle:**
- Each cycle of 6 shapes contains 1 Green Plus.

2. **Determine How Many Complete Cycles Fit into 400 Shapes:**
- \( \frac{400}{6} = 66 \text{ complete cycles} \) with a remainder of 4 shapes.

3. **Calculate the Number of Plus Signs in these Cycles:**
- In each complete cycle, there is 1 plus sign.
- Number of plus signs in 66 cycles: \( 66 \times 1 = 66 \)

4. **Consider the Remaining Shapes (after 66 Full Cycles):**
- Remaining shapes: 4 (after 396 shapes, 4 more shapes are considered)
- Check these remaining shapes: Green Plus, Purple Diamond, Orange Star, Orange Star (1 plus sign from these 4 shapes)

5. **

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