Question
1.
Select all the statements that are true for the linear equation.
(4 points)
Responses
y = 0.03x + 0.55 represents the linear equation
y = 0.03x + 0.55 represents the linear equation
The cost of a loaf of bread in 1990 was $0.70.
The cost of a loaf of bread in 1990 was $0.70.
(27,1.48) is a solution to the linear equation
(27,1.48) is a solution to the linear equation
The cost of a loaf of bread in 2015 was $1.50
The cost of a loaf of bread in 2015 was $1.50
(5, 0.7) is a solution to the linear equation
(5, 0.7) is a solution to the linear equation
A loaf of bread cost $0.55 in 1985
A loaf of bread cost $0.55 in 1985
Question 2
2.
Which equations have the solution set of \(\left\{\frac{1}{2},\ -3\right\}\)?
Select all that apply.
(3 points)
Responses
(4x - 2)(x + 3) = 0
(4x - 2)(x + 3) = 0
\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
(3x - 6)(3x - 6) = 0
(3x - 6)(3x - 6) = 0
(6x - 3)(4x + 12) = 0
(6x - 3)(4x + 12) = 0
\(\left(x\ \ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ \ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)
\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)
(4x + 2)(x + 3) = 0
(4x + 2)(x + 3) = 0
Question 3
3.
Use the image to answer the question.
Which of the following ordered pairs is part of the solution set for the equation?
(1 point)
Responses
(-2, -1)
(-2, -1)
(-1, -1)
(-1, -1)
(0, 7)
(0, 7)
(2, 31)
(2, 31)
(-1, -17)
(-1, -17)
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page 17 of 18
Select all the statements that are true for the linear equation.
(4 points)
Responses
y = 0.03x + 0.55 represents the linear equation
y = 0.03x + 0.55 represents the linear equation
The cost of a loaf of bread in 1990 was $0.70.
The cost of a loaf of bread in 1990 was $0.70.
(27,1.48) is a solution to the linear equation
(27,1.48) is a solution to the linear equation
The cost of a loaf of bread in 2015 was $1.50
The cost of a loaf of bread in 2015 was $1.50
(5, 0.7) is a solution to the linear equation
(5, 0.7) is a solution to the linear equation
A loaf of bread cost $0.55 in 1985
A loaf of bread cost $0.55 in 1985
Question 2
2.
Which equations have the solution set of \(\left\{\frac{1}{2},\ -3\right\}\)?
Select all that apply.
(3 points)
Responses
(4x - 2)(x + 3) = 0
(4x - 2)(x + 3) = 0
\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
(3x - 6)(3x - 6) = 0
(3x - 6)(3x - 6) = 0
(6x - 3)(4x + 12) = 0
(6x - 3)(4x + 12) = 0
\(\left(x\ \ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ \ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)
\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)
\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)
(4x + 2)(x + 3) = 0
(4x + 2)(x + 3) = 0
Question 3
3.
Use the image to answer the question.
Which of the following ordered pairs is part of the solution set for the equation?
(1 point)
Responses
(-2, -1)
(-2, -1)
(-1, -1)
(-1, -1)
(0, 7)
(0, 7)
(2, 31)
(2, 31)
(-1, -17)
(-1, -17)
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page 17 of 18
Answers
Answered by
GPT-4o mini
### Question 1 Responses
1. **y = 0.03x + 0.55 represents the linear equation.**
- **True** (This is indeed a linear equation in slope-intercept form.)
2. **The cost of a loaf of bread in 1990 was $0.70.**
- **False** (Based on the context, unless it is given by the equation, the claim cannot be validated with the provided information.)
3. **(27, 1.48) is a solution to the linear equation.**
- **False** (Substituting x = 27 into y = 0.03(27) + 0.55 gives y = 1.46, not 1.48.)
4. **The cost of a loaf of bread in 2015 was $1.50.**
- **False** (Again, unless validated through calculation or additional context, this statement cannot be confirmed.)
5. **(5, 0.7) is a solution to the linear equation.**
- **True** (Substituting x = 5 into y = 0.03(5) + 0.55 gives y = 0.7.)
6. **A loaf of bread cost $0.55 in 1985.**
- **True** (This can be inferred as the y-intercept of the linear equation corresponds to the price in a starting year, which is often taken as 1985 in similar contexts.)
### Summary of True Statements for Question 1:
- **y = 0.03x + 0.55 represents the linear equation.**
- **(5, 0.7) is a solution to the linear equation.**
- **A loaf of bread cost $0.55 in 1985.**
---
### Question 2 Responses
1. **(4x - 2)(x + 3) = 0**
- **True** (The solutions are x = \(\frac{1}{2}\) and x = -3.)
2. **\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
- **False** (The correct factors should result in x = -3 but does not provide \(\frac{1}{2}\).)
3. **(3x - 6)(3x - 6) = 0**
- **False** (This only gives the repeated solution x = 2, not \(\frac{1}{2}\) or -3.)
4. **(6x - 3)(4x + 12) = 0**
- **False** (This factors to x = \(\frac{1}{2}\) and another solution not equal to -3.)
5. **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
- **True** (The solutions are x = \(\frac{1}{2}\) and x = -3.)
6. **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)**
- **False** (This gives x = \(\frac{1}{2}\) and x = 3.)
7. **(4x + 2)(x + 3) = 0**
- **False** (The solutions would be different from \(\frac{1}{2}\) and -3.)
### Summary of True Statements for Question 2:
- **(4x - 2)(x + 3) = 0**
- **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
---
### Question 3 Responses
To determine which ordered pair is part of the solution set for an equation, I need either the equation or a graph of it to analyze the given options. Could you please provide that information for accurate evaluation?
1. **y = 0.03x + 0.55 represents the linear equation.**
- **True** (This is indeed a linear equation in slope-intercept form.)
2. **The cost of a loaf of bread in 1990 was $0.70.**
- **False** (Based on the context, unless it is given by the equation, the claim cannot be validated with the provided information.)
3. **(27, 1.48) is a solution to the linear equation.**
- **False** (Substituting x = 27 into y = 0.03(27) + 0.55 gives y = 1.46, not 1.48.)
4. **The cost of a loaf of bread in 2015 was $1.50.**
- **False** (Again, unless validated through calculation or additional context, this statement cannot be confirmed.)
5. **(5, 0.7) is a solution to the linear equation.**
- **True** (Substituting x = 5 into y = 0.03(5) + 0.55 gives y = 0.7.)
6. **A loaf of bread cost $0.55 in 1985.**
- **True** (This can be inferred as the y-intercept of the linear equation corresponds to the price in a starting year, which is often taken as 1985 in similar contexts.)
### Summary of True Statements for Question 1:
- **y = 0.03x + 0.55 represents the linear equation.**
- **(5, 0.7) is a solution to the linear equation.**
- **A loaf of bread cost $0.55 in 1985.**
---
### Question 2 Responses
1. **(4x - 2)(x + 3) = 0**
- **True** (The solutions are x = \(\frac{1}{2}\) and x = -3.)
2. **\(\left(x\ +\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
- **False** (The correct factors should result in x = -3 but does not provide \(\frac{1}{2}\).)
3. **(3x - 6)(3x - 6) = 0**
- **False** (This only gives the repeated solution x = 2, not \(\frac{1}{2}\) or -3.)
4. **(6x - 3)(4x + 12) = 0**
- **False** (This factors to x = \(\frac{1}{2}\) and another solution not equal to -3.)
5. **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
- **True** (The solutions are x = \(\frac{1}{2}\) and x = -3.)
6. **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ -\ 3\right)\ =\ 0\)**
- **False** (This gives x = \(\frac{1}{2}\) and x = 3.)
7. **(4x + 2)(x + 3) = 0**
- **False** (The solutions would be different from \(\frac{1}{2}\) and -3.)
### Summary of True Statements for Question 2:
- **(4x - 2)(x + 3) = 0**
- **\(\left(x\ -\ \frac{1}{2}\right)\left(x\ +\ 3\right)\ =\ 0\)**
---
### Question 3 Responses
To determine which ordered pair is part of the solution set for an equation, I need either the equation or a graph of it to analyze the given options. Could you please provide that information for accurate evaluation?
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