Question
se the image to answer the question.
The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.
This graph shows the inequality 25x+15y≥200
, and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?
(1 point)
Responses
None of the points are a viable solution.
None of the points are a viable solution.
(10,10)
left parenthesis 10 comma 10 right parenthesis
(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis
(2,3)
The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.
This graph shows the inequality 25x+15y≥200
, and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?
(1 point)
Responses
None of the points are a viable solution.
None of the points are a viable solution.
(10,10)
left parenthesis 10 comma 10 right parenthesis
(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis
(2,3)
Answers
Answer
I just need 1 answer bot
Answered by
GPT-4o mini
To determine which of the labeled points is a viable solution for the inequality \(25x + 15y \geq 200\), we need to substitute each point into the inequality.
1. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), this point satisfies the inequality.
2. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \(672.5 \geq 200\), this point also satisfies the inequality.
3. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \(95 < 200\), this point does not satisfy the inequality.
Based on these calculations, both points \( (10, 10) \) and \( (20, 11.5) \) are viable solutions that satisfy the inequality \( 25x + 15y \geq 200 \).
Since the question asks which of the labeled points is a viable solution, the correct responses are:
- **(10, 10)**
- **(20, 11.5)**
Since the test appears to be multiple choice and only one answer can be selected, you should select either \( (10, 10) \) or \( (20, 11.5) \), depending on what they are asking for in terms of viability. However, since both satisfy the inequality, officially there are viable solutions.
1. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), this point satisfies the inequality.
2. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \(672.5 \geq 200\), this point also satisfies the inequality.
3. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \(95 < 200\), this point does not satisfy the inequality.
Based on these calculations, both points \( (10, 10) \) and \( (20, 11.5) \) are viable solutions that satisfy the inequality \( 25x + 15y \geq 200 \).
Since the question asks which of the labeled points is a viable solution, the correct responses are:
- **(10, 10)**
- **(20, 11.5)**
Since the test appears to be multiple choice and only one answer can be selected, you should select either \( (10, 10) \) or \( (20, 11.5) \), depending on what they are asking for in terms of viability. However, since both satisfy the inequality, officially there are viable solutions.
Answered by
GPT-4o mini
Understood! The response with just one viable solution is:
**(10, 10)**
This point satisfies the inequality \(25x + 15y \geq 200\).
**(10, 10)**
This point satisfies the inequality \(25x + 15y \geq 200\).
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