Use the table to answer the question.

Question

Use the table to answer the question.

Table of Values

x
𝑥
ya yb
0 3 18
1 6 1312
2 9 9
Which of the following systems of linear equations does the table of values represent?

(1 point)
Responses

{y=−3x+3y=412x+18
{
𝑦
=
−
3
𝑥
+
3
𝑦
=
4
1
2
𝑥
+
18

{y=3x+3y=−412x+18
{
𝑦
=
3
𝑥
+
3
𝑦
=
−
4
1
2
𝑥
+
18

{y=3x+3y=412x+18
{
𝑦
=
3
𝑥
+
3
𝑦
=
4
1
2
𝑥
+
18

{y=3x+3y=412x−18
{
𝑦
=
3
𝑥
+
3
𝑦
=
4
1
2
𝑥
−
18

👇

7 answers
(click or scroll down)

👇

Answer 1

Bot GPT 4-o mini answered
3 days ago

To determine which system of linear equations corresponds to the table of values, we can analyze the relationship between \(x\) and \(y_a\) and between \(x\) and \(y_b\).

### Analyzing \(y_a\):
1. Given the points:
- \( (0, 3) \)
- \( (1, 6) \)
- \( (2, 9) \)

2. We can compute the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
- Using points \( (0, 3) \) and \( (1, 6) \):
\[
m = \frac{6 - 3}{1 - 0} = \frac{3}{1} = 3
\]
- Using points \( (1, 6) \) and \( (2, 9) \):
\[
m = \frac{9 - 6}{2 - 1} = \frac{3}{1} = 3
\]

3. The linear equation can be formulated as:
\[
y_a = 3x + b
\]
To find \(b\), we can use one of the points, say \( (0, 3) \):
\[
3 = 3(0) + b \implies b = 3
\]
The equation is:
\[
y_a = 3x + 3
\]

### Analyzing \(y_b\):
1. Given the points:
- \( (0, 18) \)
- \( (1, 1312) \)
- \( (2, 9) \)

2. Calculate the slope (only using points \( (1, 1312) \) and \( (2, 9) \)):
\[
m = \frac{9 - 1312}{2 - 1} = 9 - 1312 = -1303
\]

The difference between consecutive \(x\) values indicates that this relationship isn't linear between all points. Instead, it would not fit within the typical case of a linear equation format. The left logic fits a point but cannot finalize due to missing equations.

Now we can look into the possible systems provided:

- The only system that matches with our \(y_a\) equation is:
\[
\{y = 3x + 3\}
\]

- The terms of \(y_b\) remain ambiguous as it should correlate in the equations proposed.

### Conclusion:
The options provided in the responses indicate the foundational structure for \(y_a\) would yield:
1. \(y = 3x + 3\) in following all those options.

So we can conclude:
**Final Answers**
- \( \{ y = 3x + 3, y = 4 \} \) follows as consistent points set with calculation of slope.

Thus the relevant system of linear equations represented by the table of values is:
**{y=3x+3, y=4}**

Answer 2

nut answered
3 days ago

Use the table to answer the question.

Table of Values

x ya yb
0 0 3
1 2 3.5
2 4 4
Which of the following systems of linear equations does the table of values represent?

(1 point)
Responses

{y=2xy=3x+12
{
𝑦
=
2
𝑥
𝑦
=
3
𝑥
+
1
2

{y=2xy=12x+3
{
𝑦
=
2
𝑥
𝑦
=
1
2
𝑥
+
3

{y=12xy=2x+3

Answer 3

Bot GPT 4-o mini answered
3 days ago

To determine which system of linear equations corresponds to the table of values, we can analyze the relationships between \(x\) and \(y_a\) and between \(x\) and \(y_b\).

### Analyzing \(y_a\):
Given the points:
- \( (0, 0) \)
- \( (1, 2) \)
- \( (2, 4) \)

1. **Calculate the slope (m)** using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
- Using points \( (0, 0) \) and \( (1, 2) \):
\[
m = \frac{2 - 0}{1 - 0} = \frac{2}{1} = 2
\]
- Using points \( (1, 2) \) and \( (2, 4) \):
\[
m = \frac{4 - 2}{2 - 1} = \frac{2}{1} = 2
\]

2. **Formulate the linear equation**:
\[
y_a = 2x + b
\]
To find \(b\), we can use one of the points, say \( (0, 0) \):
\[
0 = 2(0) + b \implies b = 0
\]
The equation is:
\[
y_a = 2x
\]

### Analyzing \(y_b\):
Given the points:
- \( (0, 3) \)
- \( (1, 3.5) \)
- \( (2, 4) \)

1. **Calculate the slope (m)**:
- Using points \( (0, 3) \) and \( (1, 3.5) \):
\[
m = \frac{3.5 - 3}{1 - 0} = \frac{0.5}{1} = 0.5
\]
- Using points \( (1, 3.5) \) and \( (2, 4) \):
\[
m = \frac{4 - 3.5}{2 - 1} = \frac{0.5}{1} = 0.5
\]

2. **Formulate the linear equation**:
\[
y_b = 0.5x + b
\]
To find \(b\), we can use the point \( (0, 3) \):
\[
3 = 0.5(0) + b \implies b = 3
\]
The equation is:
\[
y_b = 0.5x + 3
\]

### Summary of the equations derived:
We have:
1. For \(y_a\): \(y = 2x\)
2. For \(y_b\): \(y = 0.5x + 3\)

### Matching with the provided options:
1. **{y = 2x, y = 3x + 12}**
2. **{y = 2x, y = 1/2x + 3}**
3. **{y = 1/2x, y = 2x + 3}**

The correct equations derived are:
- \(y_a = 2x\)
- \(y_b = 0.5x + 3\)

So the option that matches these equations is:
**{y = 2x, y = 1/2x + 3}**

Answer 4

nut answered
3 days ago

Use the image to answer the question.

What is the system of equations shown in the graph?

(1 point)
Responses

{y=2x+3y=3x+4
enlarged left brace start layout first row y equals 2 x plus 3 second row y equals 3 x plus 4 end layout

{y=−x+1y=2x+7
enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout

{y=3x+2y=4x+3
enlarged left btrace start layout first row y equals 3 x plus 2 second row y equals 4 x plus 3 end layout

{y=2x−3y=3x−4
enlraged left brace start layout first row y equals 2 x minus 3 second row y equals 3 x minus 4 end layout

Answer 5

Bot GPT 4-o mini answered
3 days ago

To determine the system of equations represented in the graph, we would typically analyze the slopes and intercepts of the lines displayed. However, since I don't have access to the images or graphs, I'll guide you on how to identify the correct system based on general approaches:

1. **Find the y-intercept**: Look for where each line crosses the y-axis. This will provide the constant term in the equation.

2. **Determine the slope**: Calculate the slope by finding another point on the line and using the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using two coordinates, you can determine the slope of the line.

3. **Formulate the equation**: Once you have the slope (m) and the y-intercept (b), you can write the line's equation in slope-intercept form (y = mx + b).

4. **Repeat for the second line**: Perform the same steps for the second line.

5. **Compare with options presented**: After deriving the equations from the graph, compare them with the provided options to identify the correct pair of equations.

Here's a brief example:
- If you observe a line that crosses the y-axis at 3 and has a slope of 2, that line would be \(y = 2x + 3\).
- If another line crosses the y-axis at 4 with a slope of 3, that line would be \(y = 3x + 4\).

### Based on Options Provided:
1. \( \{y=2x+3, y=3x+4\} \)
2. \( \{y=-x+1, y=2x+7\} \)
3. \( \{y=3x+2, y=4x+3\} \)
4. \( \{y=2x-3, y=3x-4\} \)

Given this process, please apply it to the graph you see, and then select the matching option based on your findings regarding the slopes and y-intercepts. If you provide results from your analysis, I'd be glad to help further!

Answer 6

nut answered
3 days ago

Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?(1 point)

Responses

{y=10−5xy=10−3x
enlarged left brace start layout first row y equals 10 minus 5 x second row y equals 10 minus 3 x end layout

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=5x−10y=3x −10
enlarged left brace start layout first row y equals 5 x minus 10 second row y equals 3 x minus 10 end layout

{y=10+5xy=10+3x

Answer 7

Bot GPT 4-o mini answered
3 days ago

To represent the situation described in your question, we need to consider the height of the eggs as they fall from a specific height (10 feet) at the specified rates.

1. **Understanding the Variables**:
- \( x \) represents the time in seconds.
- \( y \) represents the height of the egg.

2. **Setting Up the Equations**:
- The initial height of the eggs is 10 feet. As they fall, their height decreases based on their rates of descent.
- For the egg falling at a rate of 5 feet per second:
\[
y = 10 - 5x
\]
This equation shows that for every second (\(x\)), the height \(y\) reduces by 5 feet.
- For the egg falling at a rate of 3 feet per second:
\[
y = 10 - 3x
\]
Similarly, this equation indicates that for every second, the height decreases by 3 feet.

3. **System of Equations**:
- Thus, the system of equations representing both scenarios can be written as:
\[
\begin{cases}
y = 10 - 5x \\
y = 10 - 3x
\end{cases}
\]

### Matching with the Provided Responses:
From the options you provided, the correct one is:
**{y=10−5x, y=10−3x}**

This system accurately represents the heights of the eggs over time based on their respective rates of descent.