Question
A dance studio in Charleston, South Carolina, charges a one-time registration fee of $53.75 and $43 per month for classes. (6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Part A: What is the equation for the cost of dance classes if y is the total cost (in dollars) for joining for a certain number of months,x y= Part B: Graph the equation using Desmos. (Link to Desmos) Part C: Determine the key feature of the function x-intercept y-intercept slope domain In the context of the problem range in the context of the problem Skip to navigation
Answers
GPT-4o mini
To address your request thoroughly, let's break it down into parts.
### Part A: Equation for the Total Cost
The total cost \( y \) for joining the dance classes can be represented by the equation:
\[ y = 43x + 53.75 \]
Where:
- \( y \) is the total cost in dollars.
- \( 43 \) is the monthly fee in dollars.
- \( x \) is the number of months you join.
- \( 53.75 \) is the one-time registration fee.
### Part B: Graphing the Equation
To graph the equation using Desmos, follow these steps:
1. Go to the [Desmos Graphing Calculator](https://www.desmos.com/calculator).
2. Enter the equation: `y = 43x + 53.75`.
3. You can adjust the viewing window to get a better look at the graph.
### Part C: Key Features of the Function
1. **X-intercept**: This is where the function intersects the x-axis (i.e., \( y = 0 \)). To find the x-intercept, set \( y \) to 0 and solve for \( x \):
\[
0 = 43x + 53.75 \implies 43x = -53.75 \implies x \approx -1.25
\]
(In the context of this problem, while the x-intercept mathematically exists, it has no practical meaning, as negative months do not make sense.)
2. **Y-intercept**: This is where the function intersects the y-axis (i.e., when \( x = 0 \)):
\[
y = 43(0) + 53.75 = 53.75
\]
Thus, the y-intercept is \( (0, 53.75) \).
3. **Slope**: The slope of the line is \( 43 \). This means that for each additional month of classes, the total cost increases by $43.
4. **Domain**: In the context of the problem, the domain is \( x \geq 0 \) because you cannot have a negative number of months.
5. **Range**: In the context of the problem, the range is \( y \geq 53.75 \) since the minimum cost (for 0 months) is the registration fee of $53.75. The cost will increase indefinitely with more months of classes.
This analysis provides a comprehensive understanding of the cost structure associated with the dance studio classes. If you need any more assistance or clarification, feel free to ask!
### Part A: Equation for the Total Cost
The total cost \( y \) for joining the dance classes can be represented by the equation:
\[ y = 43x + 53.75 \]
Where:
- \( y \) is the total cost in dollars.
- \( 43 \) is the monthly fee in dollars.
- \( x \) is the number of months you join.
- \( 53.75 \) is the one-time registration fee.
### Part B: Graphing the Equation
To graph the equation using Desmos, follow these steps:
1. Go to the [Desmos Graphing Calculator](https://www.desmos.com/calculator).
2. Enter the equation: `y = 43x + 53.75`.
3. You can adjust the viewing window to get a better look at the graph.
### Part C: Key Features of the Function
1. **X-intercept**: This is where the function intersects the x-axis (i.e., \( y = 0 \)). To find the x-intercept, set \( y \) to 0 and solve for \( x \):
\[
0 = 43x + 53.75 \implies 43x = -53.75 \implies x \approx -1.25
\]
(In the context of this problem, while the x-intercept mathematically exists, it has no practical meaning, as negative months do not make sense.)
2. **Y-intercept**: This is where the function intersects the y-axis (i.e., when \( x = 0 \)):
\[
y = 43(0) + 53.75 = 53.75
\]
Thus, the y-intercept is \( (0, 53.75) \).
3. **Slope**: The slope of the line is \( 43 \). This means that for each additional month of classes, the total cost increases by $43.
4. **Domain**: In the context of the problem, the domain is \( x \geq 0 \) because you cannot have a negative number of months.
5. **Range**: In the context of the problem, the range is \( y \geq 53.75 \) since the minimum cost (for 0 months) is the registration fee of $53.75. The cost will increase indefinitely with more months of classes.
This analysis provides a comprehensive understanding of the cost structure associated with the dance studio classes. If you need any more assistance or clarification, feel free to ask!