Asked by kira jones
4 of 54 of 5 Items
Question
Use the image to answer the question.
A graph with the x-axis representing oranges ranging from 0 to 36 in increments of 3 and the y-axis representing dollars ranging from 0 to 20 in increments of 1 shows six plotted points, 3 each for option A and option B. Option A has the following points: left parenthesis 12 comma 5 right parenthesis; left parenthesis 24 comma 10 right parenthesis; and left parenthesis 36 comma 15 right parenthesis. Option B has the following points: left parenthesis 9 comma 6 right parenthesis; left parenthesis 18 comma 12 right parenthesis; and left parenthesis 27 comma 18 right parenthesis.
Which coordinate pair should be plotted next for Option B to keep the ratio the same?
(1 point)
Responses
(33, 24)
left parenthesis 33 comma 24 right parenthesis
(29, 20)
left parenthesis 29 comma 20 right parenthesis
(30, 21)
left parenthesis 30 comma 21 right parenthesis
(36, 24)
left parenthesis 36 comma 24 right parenthesis
Skip to navigation
page 8 of 8
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which coordinate pair should be plotted next for Option B to maintain the same ratio observed in the existing points, we should first analyze the ratio of oranges to dollars in the existing points of Option B:
1. Point (9, 6) gives us a ratio of \( \frac{6}{9} = \frac{2}{3} \).
2. Point (18, 12) gives us a ratio of \( \frac{12}{18} = \frac{2}{3} \).
3. Point (27, 18) gives us a ratio of \( \frac{18}{27} = \frac{2}{3} \).
The constant ratio for Option B is \( \frac{2}{3} \), meaning for every 3 units of oranges, there are 2 units of dollars.
To find the next point, we can use the formula derived from this ratio:
\[
\text{Dollars} = \frac{2}{3} \times \text{Oranges}
\]
Now, let's analyze the potential options:
1. For \( (33, 24) \):
\[
\frac{24}{33} \approx 0.727 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
2. For \( (29, 20) \):
\[
\frac{20}{29} \approx 0.690 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
3. For \( (30, 21) \):
\[
\frac{21}{30} = \frac{7}{10} \approx 0.700 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
4. For \( (36, 24) \):
\[
\frac{24}{36} = \frac{2}{3} \quad (\text{this one fits!})
\]
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is:
\[
\text{(36, 24)}
\]
1. Point (9, 6) gives us a ratio of \( \frac{6}{9} = \frac{2}{3} \).
2. Point (18, 12) gives us a ratio of \( \frac{12}{18} = \frac{2}{3} \).
3. Point (27, 18) gives us a ratio of \( \frac{18}{27} = \frac{2}{3} \).
The constant ratio for Option B is \( \frac{2}{3} \), meaning for every 3 units of oranges, there are 2 units of dollars.
To find the next point, we can use the formula derived from this ratio:
\[
\text{Dollars} = \frac{2}{3} \times \text{Oranges}
\]
Now, let's analyze the potential options:
1. For \( (33, 24) \):
\[
\frac{24}{33} \approx 0.727 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
2. For \( (29, 20) \):
\[
\frac{20}{29} \approx 0.690 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
3. For \( (30, 21) \):
\[
\frac{21}{30} = \frac{7}{10} \approx 0.700 \quad (\text{not } \frac{2}{3} \approx 0.667)
\]
4. For \( (36, 24) \):
\[
\frac{24}{36} = \frac{2}{3} \quad (\text{this one fits!})
\]
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is:
\[
\text{(36, 24)}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.