Question
Use the table to answer the question.
x y
0 −10
1 −9
2 −8
3 −7
Using function notation, what is the equation described in the table?(1 point)
f(x)=.......x+
x y
0 −10
1 −9
2 −8
3 −7
Using function notation, what is the equation described in the table?(1 point)
f(x)=.......x+
Answers
Answer
Use the image to answer the question.
Two side-by-side shaded ovals labeled x and y each display a list of values. Five arrows point from the values in the left oval, x, to the values in the right oval, y.
This map shows ordered pairs that belong to the function f(x)=x2
. What is the missing value?
(1 point)
Two side-by-side shaded ovals labeled x and y each display a list of values. Five arrows point from the values in the left oval, x, to the values in the right oval, y.
This map shows ordered pairs that belong to the function f(x)=x2
. What is the missing value?
(1 point)
Answer
What number would be output when an input of 4 is evaluated using the rule shown in the image? Enter your response in the output box. (1 point)
input 4 rule multiply by three then add one what is the output
input 4 rule multiply by three then add one what is the output
Answer
The number of bugs doubles every 4 days. If the bug population starts with 6 bugs, then the equation A(t)=6(2)0.25t
can represent the number of bugs. Find the value for A(8)
.(1 point)
The number of bugs after 8 days is
.
can represent the number of bugs. Find the value for A(8)
.(1 point)
The number of bugs after 8 days is
.
Answer
The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h
represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 312
hours of traveling. Enter your response in decimal form.(1 point)
The distance that you have left to travel is
miles.
represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 312
hours of traveling. Enter your response in decimal form.(1 point)
The distance that you have left to travel is
miles.
Answered by
GPT-4o mini
To find the equation that describes the relation between \( x \) and \( y \) in the table, we first observe the pattern in the values:
\[
\begin{align*}
x = 0 & \Rightarrow y = -10 \\
x = 1 & \Rightarrow y = -9 \\
x = 2 & \Rightarrow y = -8 \\
x = 3 & \Rightarrow y = -7 \\
\end{align*}
\]
From the table, we can see that as \( x \) increases by 1, \( y \) increases by 1. This indicates a linear relationship with a slope of \( 1 \).
Now, we can start with the equation of a line in the form:
\[
y = mx + b
\]
Where:
- \( m \) is the slope
- \( b \) is the y-intercept
Here, the slope \( m \) is \( 1 \). Next, we can find the y-intercept \( b \) by substituting one of the points. Using the first point \( (0, -10) \):
\[
-10 = 1(0) + b \implies b = -10
\]
Thus, the equation of the line in standard form is:
\[
y = 1x - 10
\]
In function notation, this can be written as:
\[
f(x) = 1x - 10
\]
Therefore, the final answer is:
\[
f(x) = x - 10
\]
\[
\begin{align*}
x = 0 & \Rightarrow y = -10 \\
x = 1 & \Rightarrow y = -9 \\
x = 2 & \Rightarrow y = -8 \\
x = 3 & \Rightarrow y = -7 \\
\end{align*}
\]
From the table, we can see that as \( x \) increases by 1, \( y \) increases by 1. This indicates a linear relationship with a slope of \( 1 \).
Now, we can start with the equation of a line in the form:
\[
y = mx + b
\]
Where:
- \( m \) is the slope
- \( b \) is the y-intercept
Here, the slope \( m \) is \( 1 \). Next, we can find the y-intercept \( b \) by substituting one of the points. Using the first point \( (0, -10) \):
\[
-10 = 1(0) + b \implies b = -10
\]
Thus, the equation of the line in standard form is:
\[
y = 1x - 10
\]
In function notation, this can be written as:
\[
f(x) = 1x - 10
\]
Therefore, the final answer is:
\[
f(x) = x - 10
\]
Answered by
GPT-4o mini
To find the missing value in the function \( f(x) = x^2 \), we need to evaluate the function for given values of \( x \). The function \( f \) takes an input \( x \) and produces the output \( y = x^2 \).
If you provide the specific values from the left oval labeled \( x \) and the corresponding output values in the right oval labeled \( y \), I can help you find the missing value.
For example, if you have these pairs:
- If \( x = 0 \), then \( y = f(0) = 0^2 = 0 \)
- If \( x = 1 \), then \( y = f(1) = 1^2 = 1 \)
- If \( x = 2 \), then \( y = f(2) = 2^2 = 4 \)
- If \( x = -1 \), then \( y = f(-1) = (-1)^2 = 1 \)
Please provide the specific values from the image so we can identify the missing output value.
If you provide the specific values from the left oval labeled \( x \) and the corresponding output values in the right oval labeled \( y \), I can help you find the missing value.
For example, if you have these pairs:
- If \( x = 0 \), then \( y = f(0) = 0^2 = 0 \)
- If \( x = 1 \), then \( y = f(1) = 1^2 = 1 \)
- If \( x = 2 \), then \( y = f(2) = 2^2 = 4 \)
- If \( x = -1 \), then \( y = f(-1) = (-1)^2 = 1 \)
Please provide the specific values from the image so we can identify the missing output value.
Answered by
GPT-4o mini
To determine the output when an input of 4 is evaluated using the given rule (multiply by three then add one), we follow these steps:
1. **Multiply by three**:
\[
4 \times 3 = 12
\]
2. **Add one**:
\[
12 + 1 = 13
\]
Therefore, the output when an input of 4 is evaluated is **13**.
1. **Multiply by three**:
\[
4 \times 3 = 12
\]
2. **Add one**:
\[
12 + 1 = 13
\]
Therefore, the output when an input of 4 is evaluated is **13**.
Answered by
GPT-4o mini
To find \( A(8) \) using the given equation \( A(t) = 6(2)^{0.25t} \), we will plug in \( t = 8 \).
1. Substitute \( t = 8 \) into the equation:
\[
A(8) = 6(2)^{0.25 \times 8}
\]
2. Calculate \( 0.25 \times 8 \):
\[
0.25 \times 8 = 2
\]
3. Now substitute this value back into the equation:
\[
A(8) = 6(2)^{2}
\]
4. Calculate \( (2)^{2} \):
\[
(2)^{2} = 4
\]
5. Finally, multiply by 6:
\[
A(8) = 6 \times 4 = 24
\]
Thus, the number of bugs after 8 days is **24**.
1. Substitute \( t = 8 \) into the equation:
\[
A(8) = 6(2)^{0.25 \times 8}
\]
2. Calculate \( 0.25 \times 8 \):
\[
0.25 \times 8 = 2
\]
3. Now substitute this value back into the equation:
\[
A(8) = 6(2)^{2}
\]
4. Calculate \( (2)^{2} \):
\[
(2)^{2} = 4
\]
5. Finally, multiply by 6:
\[
A(8) = 6 \times 4 = 24
\]
Thus, the number of bugs after 8 days is **24**.
Answered by
GPT-4o mini
To find the distance left to get to Bloomsfield after traveling for \( h = 312 \) hours, we can use the given function:
\[
D(h) = 440 - 65h
\]
Substituting \( h = 312 \) into the equation:
\[
D(312) = 440 - 65 \times 312
\]
Now, we perform the multiplication:
\[
65 \times 312 = 20280
\]
Then, substitute this value back into the equation:
\[
D(312) = 440 - 20280
\]
Now, perform the subtraction:
\[
D(312) = 440 - 20280 = -19840
\]
Therefore, the distance that you have left to travel after 312 hours is **-19840** miles.
This negative value indicates that you have already passed Bloomsfield and are 19840 miles beyond it. If you're looking specifically for the absolute distance beyond Bloomsfield, it would be 19840 miles in the opposite direction.
\[
D(h) = 440 - 65h
\]
Substituting \( h = 312 \) into the equation:
\[
D(312) = 440 - 65 \times 312
\]
Now, we perform the multiplication:
\[
65 \times 312 = 20280
\]
Then, substitute this value back into the equation:
\[
D(312) = 440 - 20280
\]
Now, perform the subtraction:
\[
D(312) = 440 - 20280 = -19840
\]
Therefore, the distance that you have left to travel after 312 hours is **-19840** miles.
This negative value indicates that you have already passed Bloomsfield and are 19840 miles beyond it. If you're looking specifically for the absolute distance beyond Bloomsfield, it would be 19840 miles in the opposite direction.
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