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Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the...Question
Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the graph, enter the values that complete the equation for this situation.
(1 point)
y=
x+
(1 point)
y=
x+
Answers
Answer
(2,30) , (4,40)
Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the graph, enter the values that complete the equation for this situation.
(1 point)
y=
x+
Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the graph, enter the values that complete the equation for this situation.
(1 point)
y=
x+
Answer
Use the table to answer the question.
x f(x)
−1
0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4 . Which of the given x values produces the largest output for the function?
(1 point)
Responses
x=1
x equals 1
x=0
x equals 0
x=−1
x equals negative 1
x=2
x f(x)
−1
0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4 . Which of the given x values produces the largest output for the function?
(1 point)
Responses
x=1
x equals 1
x=0
x equals 0
x=−1
x equals negative 1
x=2
Answered by
GPT-4o mini
To complete the equation \( y = mx + b \) for Luis's paddleboat rental situation, we need to identify two key pieces of information from the graph:
1. The hourly fee (m), which represents the slope of the line, and
2. The deposit (b), which is the y-intercept, or the initial amount he pays even before he starts using the paddleboat.
Since I cannot see the graph, please provide the hourly fee and the total deposit amount, and I can help you fill in the equation with those values. For example, if the hourly fee is $5 and the deposit is $10, the equation would be:
\[ y = 5x + 10 \]
Where \( y \) is the total cost, \( x \) is the number of hours the paddleboat is rented, 5 is the hourly fee, and 10 is the deposit. Let me know the values, and I'll assist you further!
1. The hourly fee (m), which represents the slope of the line, and
2. The deposit (b), which is the y-intercept, or the initial amount he pays even before he starts using the paddleboat.
Since I cannot see the graph, please provide the hourly fee and the total deposit amount, and I can help you fill in the equation with those values. For example, if the hourly fee is $5 and the deposit is $10, the equation would be:
\[ y = 5x + 10 \]
Where \( y \) is the total cost, \( x \) is the number of hours the paddleboat is rented, 5 is the hourly fee, and 10 is the deposit. Let me know the values, and I'll assist you further!
Answered by
GPT-4o mini
To derive the equation from the points (2, 30) and (4, 40), we can first determine the slope (m) and then find the y-intercept (b).
1. **Calculate the slope (m):**
Using the formula for slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 30) and (4, 40):
\[
m = \frac{40 - 30}{4 - 2} = \frac{10}{2} = 5
\]
So, the hourly fee is $5.
2. **Find the y-intercept (b):**
We can use one of the points to find b. We'll use the point (2, 30):
Using the equation of a line \( y = mx + b \):
\[
30 = 5(2) + b
\]
\[
30 = 10 + b
\]
\[
b = 30 - 10 = 20
\]
So, the deposit is $20.
3. **Complete the equation:**
Now we can write the equation:
\[
y = 5x + 20
\]
Thus, the completed equation for this situation is:
**y = 5x + 20**.
1. **Calculate the slope (m):**
Using the formula for slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 30) and (4, 40):
\[
m = \frac{40 - 30}{4 - 2} = \frac{10}{2} = 5
\]
So, the hourly fee is $5.
2. **Find the y-intercept (b):**
We can use one of the points to find b. We'll use the point (2, 30):
Using the equation of a line \( y = mx + b \):
\[
30 = 5(2) + b
\]
\[
30 = 10 + b
\]
\[
b = 30 - 10 = 20
\]
So, the deposit is $20.
3. **Complete the equation:**
Now we can write the equation:
\[
y = 5x + 20
\]
Thus, the completed equation for this situation is:
**y = 5x + 20**.
Answered by
GPT-4o mini
To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate the value of \( f(x) \) for each given \( x \) value: -1, 0, 1, and 2.
1. For \( x = -1 \):
\[
f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 4
\]
2. For \( x = 0 \):
\[
f(0) = -((0) + 1)^2 + 4 = -1^2 + 4 = -1 + 4 = 3
\]
3. For \( x = 1 \):
\[
f(1) = -((1) + 1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0
\]
4. For \( x = 2 \):
\[
f(2) = -((2) + 1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5
\]
Now, we can summarize the output values:
| x | f(x) |
|-----|------|
| -1 | 4 |
| 0 | 3 |
| 1 | 0 |
| 2 | -5 |
### Largest Output:
The largest output value from this function occurs when \( x = -1 \), yielding \( f(-1) = 4 \).
Therefore, the response is:
**x = -1**
1. For \( x = -1 \):
\[
f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 4
\]
2. For \( x = 0 \):
\[
f(0) = -((0) + 1)^2 + 4 = -1^2 + 4 = -1 + 4 = 3
\]
3. For \( x = 1 \):
\[
f(1) = -((1) + 1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0
\]
4. For \( x = 2 \):
\[
f(2) = -((2) + 1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5
\]
Now, we can summarize the output values:
| x | f(x) |
|-----|------|
| -1 | 4 |
| 0 | 3 |
| 1 | 0 |
| 2 | -5 |
### Largest Output:
The largest output value from this function occurs when \( x = -1 \), yielding \( f(-1) = 4 \).
Therefore, the response is:
**x = -1**
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