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For the diagram below, the table gives the total number of small triangles y in figure number x. What pattern can you table? Represent the relationship using words, an equation, and a graph. Figure Number, x Tria 444 Figure 1 3 Figure 2 4 Figure 3 Represent the relationship in words. Choose the correct answer below. O A. The total number of small triangles y is five times the figure number x O B. The total number of small triangles y is three times the square of the figure number x. O C. The total number of small triangles y is three raised to the figure number x. O D. The total number of small triangles y is the square of the figure number x.

For the diagram below, the table gives the total number of small triangles y in figure number x. What pattern can you table? Represent the relationship using words, an equation, and a graph. Figure Number, x Tria 444 Figure 1 3 Figure 2 4 Figure 3 Represent the relationship in words. Choose the correct answer below. O A. The total number of small triangles y is five times the figure number x O B. The total number of small triangles y is three times the square of the figure number x. O C. The total number of small triangles y is three raised to the figure number x. O D. The total number of small triangles y is the square of the figure number x.

Algebra and Trigonometry (6th Edition)
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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**Transcription and Explanation for Educational Website:** ### Understanding Patterns with Triangles In the diagram shown, we explore how the number of small triangles increases in each successive figure. We aim to find a pattern and then express this relationship using words and equations. #### Diagrams: - **Figure 1**: Contains 3 small triangles. - **Figure 2**: Contains 12 small triangles. - **Figure 3**: Contains 27 small triangles. #### Table of Values: - **Figure Number (x)** | **Total Small Triangles (y)** | **Ordered Pair (x, y)** - 1 | 3 | (1, 3) - 2 | 12 | (2, 12) - 3 | 27 | (3, 27) - 4 | ? | ? #### Multiple Choice: Determine the relationship between the figure number and the total number of small triangles. - **A.** The total number of small triangles \( y \) is five times the figure number \( x \). - **B.** The total number of small triangles \( y \) is three times the square of the figure number \( x \). - **C.** The total number of small triangles \( y \) is three raised to the figure number \( x \). - **D.** The total number of small triangles \( y \) is the square of the figure number \( x \). ### Explanation: To understand this relationship, notice how the number of triangles grows with the figure number. Use the options to identify which description matches the pattern. Explore these patterns further to develop skills in pattern recognition, algebraic expressions, and mathematical reasoning. (Note: Option completion and explanation of graphs require further input or exploration.)
Transcribed Image Text:**Transcription and Explanation for Educational Website:** ### Understanding Patterns with Triangles In the diagram shown, we explore how the number of small triangles increases in each successive figure. We aim to find a pattern and then express this relationship using words and equations. #### Diagrams: - **Figure 1**: Contains 3 small triangles. - **Figure 2**: Contains 12 small triangles. - **Figure 3**: Contains 27 small triangles. #### Table of Values: - **Figure Number (x)** | **Total Small Triangles (y)** | **Ordered Pair (x, y)** - 1 | 3 | (1, 3) - 2 | 12 | (2, 12) - 3 | 27 | (3, 27) - 4 | ? | ? #### Multiple Choice: Determine the relationship between the figure number and the total number of small triangles. - **A.** The total number of small triangles \( y \) is five times the figure number \( x \). - **B.** The total number of small triangles \( y \) is three times the square of the figure number \( x \). - **C.** The total number of small triangles \( y \) is three raised to the figure number \( x \). - **D.** The total number of small triangles \( y \) is the square of the figure number \( x \). ### Explanation: To understand this relationship, notice how the number of triangles grows with the figure number. Use the options to identify which description matches the pattern. Explore these patterns further to develop skills in pattern recognition, algebraic expressions, and mathematical reasoning. (Note: Option completion and explanation of graphs require further input or exploration.)
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