We appreciate your visit to For a wrestler to qualify in his weight class he needs to weigh more than 165 pounds but less than or equal to 185 pounds. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the correct inequality model for the problem, we need to establish the condition where the wrestler's weight fits within the given weight class, specifically between more than 165 pounds and less than or equal to 185 pounds.
Let's break this down:
1. Current Situation:
- The wrestler weighs 189 pounds currently.
2. Weight Loss Rate:
- He is losing 0.5 pounds per week.
3. Required Weight Range:
- The wrestler's weight needs to be greater than 165 pounds but less than or equal to 185 pounds.
4. Set Up the Inequality:
- Use the formula: [tex]\( \text{current weight} - \text{(weight loss per week)} \times w \)[/tex]
- Plug in values we know: [tex]\( 189 - 0.5w \)[/tex]
5. Establish the Conditions:
- For the lower bound: The weight must be more than 165 pounds.
- [tex]\( 165 < 189 - 0.5w \)[/tex]
- For the upper bound: The weight must be less than or equal to 185 pounds.
- [tex]\( 189 - 0.5w \leq 185 \)[/tex]
6. Combine the Inequalities:
- Here we combine both conditions to ensure the wrestler falls within the qualifying range:
- [tex]\( 165 < 189 - 0.5w \leq 185 \)[/tex]
Thus, the correct inequality modeling the number of weeks he must lose weight to qualify is:
165 < 189 - 0.5w ≤ 185
This inequality ensures that the wrestler's weight after losing weight for [tex]\( w \)[/tex] weeks is within the specified range required for qualification.
Let's break this down:
1. Current Situation:
- The wrestler weighs 189 pounds currently.
2. Weight Loss Rate:
- He is losing 0.5 pounds per week.
3. Required Weight Range:
- The wrestler's weight needs to be greater than 165 pounds but less than or equal to 185 pounds.
4. Set Up the Inequality:
- Use the formula: [tex]\( \text{current weight} - \text{(weight loss per week)} \times w \)[/tex]
- Plug in values we know: [tex]\( 189 - 0.5w \)[/tex]
5. Establish the Conditions:
- For the lower bound: The weight must be more than 165 pounds.
- [tex]\( 165 < 189 - 0.5w \)[/tex]
- For the upper bound: The weight must be less than or equal to 185 pounds.
- [tex]\( 189 - 0.5w \leq 185 \)[/tex]
6. Combine the Inequalities:
- Here we combine both conditions to ensure the wrestler falls within the qualifying range:
- [tex]\( 165 < 189 - 0.5w \leq 185 \)[/tex]
Thus, the correct inequality modeling the number of weeks he must lose weight to qualify is:
165 < 189 - 0.5w ≤ 185
This inequality ensures that the wrestler's weight after losing weight for [tex]\( w \)[/tex] weeks is within the specified range required for qualification.
Thanks for taking the time to read For a wrestler to qualify in his weight class he needs to weigh more than 165 pounds but less than or equal to 185 pounds. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
