Use the image to answer the question.

Question

Use 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

(2,3)
left parenthesis 2 comma 3 right parenthesis

None of the points are a viable solution.
None of the points are a viable solution.

(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis

(10,10)

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine which labeled point is a viable solution for Lina’s earnings represented by the inequality \( 25x + 15y \geq 200 \), we will substitute each of the given points into the inequality and check if they satisfy it.

1. **Point (2, 3):**
- Substitute \( x = 2 \) and \( y = 3 \):
\[
25(2) + 15(3) = 50 + 45 = 95
\]
- Check: \( 95 \geq 200 \) (False)

2. **Point (20, 11.5):**
- Substitute \( x = 20 \) and \( y = 11.5 \):
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
- Check: \( 672.5 \geq 200 \) (True)

3. **Point (10, 10):**
- Substitute \( x = 10 \) and \( y = 10 \):
\[
25(10) + 15(10) = 250 + 150 = 400
\]
- Check: \( 400 \geq 200 \) (True)

After evaluating all points:

- (2, 3) is not a viable solution.
- (20, 11.5) is a viable solution.
- (10, 10) is a viable solution.

**Conclusion:** The labeled point (20, 11.5) is a viable solution for the inequality \( 25x + 15y \geq 200 \).