The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side is 15 yards longer than the other side. Which equations model these conditions if x is one of the dimensions of the playground? Select all that apply. OX- 15 = 324 OX x+15) = 324 OXx-15) = 324 OX+ 15 x- 324 = 0 O(x+7.5)( x- 7.5) = 324
The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side is 15 yards longer than the other side. Which equations model these conditions if x is one of the dimensions of the playground? Select all that apply. OX- 15 = 324 OX x+15) = 324 OXx-15) = 324 OX+ 15 x- 324 = 0 O(x+7.5)( x- 7.5) = 324
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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![### Problem Statement
Select all that apply.
The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side is 15 yards longer than the other side. Which equations model these conditions if \( x \) is one of the dimensions of the playground? Select all that apply.
Options:
- [ ] \( x^2 - 15 = 324 \)
- [ ] \( x(x + 15) = 324 \)
- [ ] \( x(x - 15) = 324 \)
- [ ] \( x^2 + 15x - 324 = 0 \)
- [ ] \( (x + 7.5)(x - 7.5) = 324 \)
### Explanation of the Options
- **Option 1:** \( x^2 - 15 = 324 \)
- This equation does not correctly describe the relationship between the dimensions given the conditions provided.
- **Option 2:** \( x(x + 15) = 324 \)
- Here, \( x \) is one side and \( x + 15 \) is the other side. The product of the two sides is the area \( 324 \).
- **Option 3:** \( x(x - 15) = 324 \)
- This option implies one side is shorter than the other by 15 units, which is opposite to the given condition.
- **Option 4:** \( x^2 + 15x - 324 = 0 \)
- This quadratic equation re-arranges \( x(x + 15) = 324 \) into standard quadratic form.
- **Option 5:** \( (x + 7.5)(x - 7.5) = 324 \)
- This option would be correct for a condition where \( x \) is 7.5 units more or less than another dimension, which is not consistent with the given condition of one side being 15 yards longer.
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Transcribed Image Text:### Problem Statement
Select all that apply.
The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side is 15 yards longer than the other side. Which equations model these conditions if \( x \) is one of the dimensions of the playground? Select all that apply.
Options:
- [ ] \( x^2 - 15 = 324 \)
- [ ] \( x(x + 15) = 324 \)
- [ ] \( x(x - 15) = 324 \)
- [ ] \( x^2 + 15x - 324 = 0 \)
- [ ] \( (x + 7.5)(x - 7.5) = 324 \)
### Explanation of the Options
- **Option 1:** \( x^2 - 15 = 324 \)
- This equation does not correctly describe the relationship between the dimensions given the conditions provided.
- **Option 2:** \( x(x + 15) = 324 \)
- Here, \( x \) is one side and \( x + 15 \) is the other side. The product of the two sides is the area \( 324 \).
- **Option 3:** \( x(x - 15) = 324 \)
- This option implies one side is shorter than the other by 15 units, which is opposite to the given condition.
- **Option 4:** \( x^2 + 15x - 324 = 0 \)
- This quadratic equation re-arranges \( x(x + 15) = 324 \) into standard quadratic form.
- **Option 5:** \( (x + 7.5)(x - 7.5) = 324 \)
- This option would be correct for a condition where \( x \) is 7.5 units more or less than another dimension, which is not consistent with the given condition of one side being 15 yards longer.
### Interactive Components
- **Next Question**
- Clicking this button will lead you to the next problem in the sequence.
- **Read Next Section**
- This button opens the following section of the educational content.
- **Ask for Help**
- Click here if you need assistance or additional explanations regarding the current problem.
- **Turn It In**
- Submit your final answer choices.
---
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