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Materials ⚫ graph paper ⚫ pencil ruler ⚫ calculator Chapters 7-9 Project Designing a Stairway OBJECTIVE Compare step measurements to see how they affect stairway design. INVESTIGATING THE DATA riser tread The horizontal part of a step is the tread, and the vertical part is the riser. The table gives the tread and riser measurements of four different stairways. Stairway Tread (in.) Riser (in.) 10 A 7 11 B 7 9 C 8 12 D 6 1. Use the measurements in the table to draw three steps for each Stairway A-D on a piece of graph paper. 2. Analyze your drawings. Which stairway is the steepest? Which stairway gives the most foot space on a step? 3. For each Stairway A-D, find the ratio of riser size to tread size Then write each ratio as a decimal rounded to the nearest tenth. What characteristic of a stairway do these ratios describe? Two generally accepted rules for designing stairways are listed below. riser tread Rule 1: The sum of one tread and one riser is from 17 inches to 18 inches. Rule 2: The sum of one tread and two risers is from 24 inches to 25 inches. 4. You can use the following linear inequalities to represent Rule 1. t + r≥ 17 and t+r≤ 18 Write linear inequalities to represent Rule 2. Then use the inequalities to show that each Stairway A-D follows one of the rules. 5. Graph the system of four inequalities on the same coordinate plane. Use the horizontal axis for t and the vertical axis for r. Then use the values in the table to label the point (t, r) for each Stairway A-D. What does each solution of the system represent? 6. Name any other point E that is a solution of the system. Give tres and rise measurements for a Stairway E that the point represents. 562 Chapter 9 Quadratic Equations and Functions

Materials ⚫ graph paper ⚫ pencil ruler ⚫ calculator Chapters 7-9 Project Designing a Stairway OBJECTIVE Compare step measurements to see how they affect stairway design. INVESTIGATING THE DATA riser tread The horizontal part of a step is the tread, and the vertical part is the riser. The table gives the tread and riser measurements of four different stairways. Stairway Tread (in.) Riser (in.) 10 A 7 11 B 7 9 C 8 12 D 6 1. Use the measurements in the table to draw three steps for each Stairway A-D on a piece of graph paper. 2. Analyze your drawings. Which stairway is the steepest? Which stairway gives the most foot space on a step? 3. For each Stairway A-D, find the ratio of riser size to tread size Then write each ratio as a decimal rounded to the nearest tenth. What characteristic of a stairway do these ratios describe? Two generally accepted rules for designing stairways are listed below. riser tread Rule 1: The sum of one tread and one riser is from 17 inches to 18 inches. Rule 2: The sum of one tread and two risers is from 24 inches to 25 inches. 4. You can use the following linear inequalities to represent Rule 1. t + r≥ 17 and t+r≤ 18 Write linear inequalities to represent Rule 2. Then use the inequalities to show that each Stairway A-D follows one of the rules. 5. Graph the system of four inequalities on the same coordinate plane. Use the horizontal axis for t and the vertical axis for r. Then use the values in the table to label the point (t, r) for each Stairway A-D. What does each solution of the system represent? 6. Name any other point E that is a solution of the system. Give tres and rise measurements for a Stairway E that the point represents. 562 Chapter 9 Quadratic Equations and Functions

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.6: Functions Defined By Tables And Graphs
Problem 10WE
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Materials ⚫ graph paper ⚫ pencil ruler ⚫ calculator Chapters 7-9 Project Designing a Stairway OBJECTIVE Compare step measurements to see how they affect stairway design. INVESTIGATING THE DATA riser tread The horizontal part of a step is the tread, and the vertical part is the riser. The table gives the tread and riser measurements of four different stairways. Stairway Tread (in.) Riser (in.) 10 A 7 11 B 7 9 C 8 12 D 6 1. Use the measurements in the table to draw three steps for each Stairway A-D on a piece of graph paper. 2. Analyze your drawings. Which stairway is the steepest? Which stairway gives the most foot space on a step? 3. For each Stairway A-D, find the ratio of riser size to tread size Then write each ratio as a decimal rounded to the nearest tenth. What characteristic of a stairway do these ratios describe? Two generally accepted rules for designing stairways are listed below. riser tread Rule 1: The sum of one tread and one riser is from 17 inches to 18 inches. Rule 2: The sum of one tread and two risers is from 24 inches to 25 inches. 4. You can use the following linear inequalities to represent Rule 1. t + r≥ 17 and t+r≤ 18 Write linear inequalities to represent Rule 2. Then use the inequalities to show that each Stairway A-D follows one of the rules. 5. Graph the system of four inequalities on the same coordinate plane. Use the horizontal axis for t and the vertical axis for r. Then use the values in the table to label the point (t, r) for each Stairway A-D. What does each solution of the system represent? 6. Name any other point E that is a solution of the system. Give tres and rise measurements for a Stairway E that the point represents. 562 Chapter 9 Quadratic Equations and Functions
Transcribed Image Text:Materials ⚫ graph paper ⚫ pencil ruler ⚫ calculator Chapters 7-9 Project Designing a Stairway OBJECTIVE Compare step measurements to see how they affect stairway design. INVESTIGATING THE DATA riser tread The horizontal part of a step is the tread, and the vertical part is the riser. The table gives the tread and riser measurements of four different stairways. Stairway Tread (in.) Riser (in.) 10 A 7 11 B 7 9 C 8 12 D 6 1. Use the measurements in the table to draw three steps for each Stairway A-D on a piece of graph paper. 2. Analyze your drawings. Which stairway is the steepest? Which stairway gives the most foot space on a step? 3. For each Stairway A-D, find the ratio of riser size to tread size Then write each ratio as a decimal rounded to the nearest tenth. What characteristic of a stairway do these ratios describe? Two generally accepted rules for designing stairways are listed below. riser tread Rule 1: The sum of one tread and one riser is from 17 inches to 18 inches. Rule 2: The sum of one tread and two risers is from 24 inches to 25 inches. 4. You can use the following linear inequalities to represent Rule 1. t + r≥ 17 and t+r≤ 18 Write linear inequalities to represent Rule 2. Then use the inequalities to show that each Stairway A-D follows one of the rules. 5. Graph the system of four inequalities on the same coordinate plane. Use the horizontal axis for t and the vertical axis for r. Then use the values in the table to label the point (t, r) for each Stairway A-D. What does each solution of the system represent? 6. Name any other point E that is a solution of the system. Give tres and rise measurements for a Stairway E that the point represents. 562 Chapter 9 Quadratic Equations and Functions
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