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Use the image to answer the question.

A coordinate plane's x-axis ranges from 0 to 4 and its y-axis ranges from 0 to 12, both by 2-unit increments. A line is plotted passing through a marked point at left parenthesis 0 comma 5 right parenthesis.

Lina charges a one-time fee of $5, plus $10 per hour, for a dog-walking appointment. Does the current graph use a reasonable scale for this situation? Enter 1 for yes or 2 for no.

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To determine if the graph uses a reasonable scale for Lina's dog-walking charges, we need to analyze the cost structure:

Lina charges a one-time fee of $5 and $10 per hour. This means the total cost can be represented by the formula:

\[ \text{Total Cost} = 5 + 10h \]

Where \( h \) is the number of hours walked.

Now let's consider the scale of the coordinate plane provided:
- The x-axis goes from 0 to 4. This could represent the number of hours (0 to 4 hours).
- The y-axis goes from 0 to 12, which would represent total cost (from $0 to $12).

Now let's calculate the total cost for different hours walked:
- If \( h = 0 \): Total Cost = \( 5 + 10(0) = 5 \)
- If \( h = 1 \): Total Cost = \( 5 + 10(1) = 15 \)
- If \( h = 2 \): Total Cost = \( 5 + 10(2) = 25 \)
- If \( h = 3 \): Total Cost = \( 5 + 10(3) = 35 \)
- If \( h = 4 \): Total Cost = \( 5 + 10(4) = 45 \)

Looking at the calculations:
- The scale on the y-axis (0 to 12) is not sufficient to capture the total costs of appointments for even 1 hour of dog walking, as that would cost $15 and go beyond the maximum limit of 12.

Since the graph does not provide a reasonable scale to represent the costs based on the number of hours walked (as costs quickly exceed the maximum y-value of 12), we conclude that the provided graph is not suitable for this situation.

So, the answer is **2** (no).

anonymous anonymous answered
1 hour ago

Use the image to answer the question.

A coordinate plane's axes range from 0 to 50, both by 10-unit increments. A diagonal line is plotted.

Sal is draining his 25-gallon fish tank at approximately half a gallon per minute and graphed the situation. Is the scale reasonable for this graph? Enter 1 for yes or 2 for no.

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To determine if the scale of the coordinate plane is reasonable for Sal’s fish tank draining situation, we need to analyze the details given.

Sal is draining a 25-gallon fish tank at a rate of approximately 0.5 gallons per minute. This means:

- The y-axis could represent the gallons of water remaining in the tank.
- The x-axis could represent the time in minutes.

Given that the coordinate plane ranges from 0 to 50 on both axes, and both axes scale by 10-unit increments, we can consider the time it takes to drain the tank:

1. **Total Volume of Tank**: 25 gallons
2. **Rate of Draining**: 0.5 gallons per minute

To find out how long it will take to drain the entire tank, we use the formula:

\[
\text{Time} = \frac{\text{Total Volume}}{\text{Rate}} = \frac{25 \text{ gallons}}{0.5 \text{ gallons/minute}} = 50 \text{ minutes}
\]

Now, analyzing the axes:
- The x-axis (time) ranges from 0 to 50 minutes, which is appropriate since it matches exactly how long it will take to drain the tank.
- The y-axis (gallons remaining) ranges from 0 to 50. Since Sal starts with 25 gallons, and it goes down to 0 gallons as time progresses, this scale also captures the necessary range.

Since the scales of both axes adequately represent the situation of draining the fish tank over time, we can conclude that the scale is reasonable.

Thus, the answer is **1** (yes).

anonymous anonymous answered
1 hour ago

The cost of taking a cab is $4 plus $0.75 per mile. This can be represented using the linear function c=0.75m+4

, where c is the cost per trip and m is the distance in miles. Graph the equation on a coordinate plane. Based on your line, what would the corresponding dependent variable be if you were to travel 4.5 miles? Round your answer to the nearest hundredth.(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To find the corresponding cost (\(c\)) when traveling 4.5 miles (\(m\)), we can use the given linear function:

\[
c = 0.75m + 4
\]

Now, substitute \(m = 4.5\) into the equation:

\[
c = 0.75(4.5) + 4
\]

Calculating \(0.75 \times 4.5\):

\[
0.75 \times 4.5 = 3.375
\]

Now, add this result to the initial fee of 4:

\[
c = 3.375 + 4 = 7.375
\]

Now, rounding to the nearest hundredth, we have:

\[
c \approx 7.38
\]

Therefore, the corresponding dependent variable (cost) for traveling 4.5 miles is **$7.38**.

anonymous anonymous answered
1 hour ago

Use the image to answer the question.

A line is plotted on a coordinate plane. The line begins in quadrant 2 sloping downward from left to right, passes through quadrant 1, and descends through quadrant 4.

Identify the y-intercept.

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

In a coordinate plane, the y-intercept of a line is the point where the line crosses the y-axis. The y-axis is represented by \( x = 0 \).

Since you mentioned that the line begins in quadrant 2 and slopes downward from left to right, this implies that:

- The line will cross the y-axis in quadrant 2.
- The y-intercept will have a positive y-coordinate (since quadrant 2 is where y-values are positive).

Although I cannot see the image, I can provide you with the general method to identify the y-intercept from the plotted line:

1. Look for the point where the line intersects the y-axis.
2. The coordinates of this intersection will be in the form \( (0, y) \), where \( y \) represents the y-coordinate of the y-intercept.

If you can provide the specific coordinates of the y-intercept from the image or describe it, I can help you identify the exact value. In most cases where the graph is given, the y-intercept coordinates should be observable directly from the plotting.

For instance, if the line crosses the y-axis at \( (0, 3) \), then the y-intercept is \( 3 \). If you were able to see the coordinates, simply read off the \( y \)-value at \( x = 0 \) to identify the y-intercept.

If you can provide the specific y-coordinate from the image, I can confirm the value for you!