Question
5.
Which equation matches the solution set of {5} ?
(1 point)
Responses
x + x - 9 = 1 + x
x + x - 9 = 1 + x
2x - 20 = 30
2x - 20 = 30
x2
- 10 = 15
x squared - 10 = 15
3x5 + 4 = 7
3x5 + 4 = 7
Question 2
6.
What is the value of p in the following equation?
20pā3 = 5
(1 point)
Responses
1
1
3
3
5
5
7
7
Question 3
7.
Which of the following equations has the solution set x = {ā95, 3}
?
(1 point)
Responses
(x - 3)(9x + 5) = 0
(x - 3)(9x + 5) = 0
-3x(5x + 9) = 0
-3x(5x + 9) = 0
(x + 3)(9x - 5) = 0
(x + 3)(9x - 5) = 0
(x - 3)(5x + 9) = 0
(x - 3)(5x + 9) = 0
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Which equation matches the solution set of {5} ?
(1 point)
Responses
x + x - 9 = 1 + x
x + x - 9 = 1 + x
2x - 20 = 30
2x - 20 = 30
x2
- 10 = 15
x squared - 10 = 15
3x5 + 4 = 7
3x5 + 4 = 7
Question 2
6.
What is the value of p in the following equation?
20pā3 = 5
(1 point)
Responses
1
1
3
3
5
5
7
7
Question 3
7.
Which of the following equations has the solution set x = {ā95, 3}
?
(1 point)
Responses
(x - 3)(9x + 5) = 0
(x - 3)(9x + 5) = 0
-3x(5x + 9) = 0
-3x(5x + 9) = 0
(x + 3)(9x - 5) = 0
(x + 3)(9x - 5) = 0
(x - 3)(5x + 9) = 0
(x - 3)(5x + 9) = 0
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Answers
GPT-4o mini
**Question 1: Which equation matches the solution set of {5}?**
To determine which equation has the solution set of {5}, we can solve each equation for \(x\) and see which one results in \(x = 5\).
1. \(x + x - 9 = 1 + x\)
\[
2x - 9 = 1 + x \\
2x - x = 1 + 9 \\
x = 10 \, \text{(not a match)}
\]
2. \(2x - 20 = 30\)
\[
2x = 30 + 20 \\
2x = 50 \\
x = 25 \, \text{(not a match)}
\]
3. \(x^2 - 10 = 15\)
\[
x^2 = 15 + 10 \\
x^2 = 25 \\
x = 5 \, \text{or} \, x = -5 \, \text{(partial match)}
\]
4. \(3x + 4 = 7\) (Note: it seems there may be a typo in how this is presented; it may mean \(3x + 4 = 7\))
\[
3x = 7 - 4 \\
3x = 3 \\
x = 1 \, \text{(not a match)}
\]
**The equation that matches the solution set {5} is**:
**\(x^2 - 10 = 15\)** (since it has a solution of \(x = 5\)).
---
**Question 2: What is the value of \(p\) in the following equation?**
Given:
\(20p - 3 = 5\)
To solve for \(p\):
\[
20p = 5 + 3 \\
20p = 8 \\
p = \frac{8}{20} \\
p = \frac{2}{5} \approx 0.4 \, \text{(not an option)}
\]
In the given options: 1, 3, 5, 7, none match our result. Please check if the equation provided is correct.
---
**Question 3: Which of the following equations has the solution set \(x = \{-95, 3\}\)?**
1. \((x - 3)(9x + 5) = 0\)
- Solutions: \(x = 3\) and \(9x + 5 = 0\) gives \(x = -\frac{5}{9}\) (not a match).
2. \(-3x(5x + 9) = 0\)
- Solutions: \(x = 0\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
3. \((x + 3)(9x - 5) = 0\)
- Solutions: \(x = -3\) and \(9x - 5 = 0\) gives \(x = \frac{5}{9}\) (not a match).
4. \((x - 3)(5x + 9) = 0\)
- Solutions: \(x = 3\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
**None of the above equations directly represent the solution set \(x = \{-95, 3\}\).** The equation that should represent this condition is:
\[
(x - 3)(x + 95) = 0
\]
This indicates that there may be an oversight in the provided options. Please recheck the equations again for correctness.
To determine which equation has the solution set of {5}, we can solve each equation for \(x\) and see which one results in \(x = 5\).
1. \(x + x - 9 = 1 + x\)
\[
2x - 9 = 1 + x \\
2x - x = 1 + 9 \\
x = 10 \, \text{(not a match)}
\]
2. \(2x - 20 = 30\)
\[
2x = 30 + 20 \\
2x = 50 \\
x = 25 \, \text{(not a match)}
\]
3. \(x^2 - 10 = 15\)
\[
x^2 = 15 + 10 \\
x^2 = 25 \\
x = 5 \, \text{or} \, x = -5 \, \text{(partial match)}
\]
4. \(3x + 4 = 7\) (Note: it seems there may be a typo in how this is presented; it may mean \(3x + 4 = 7\))
\[
3x = 7 - 4 \\
3x = 3 \\
x = 1 \, \text{(not a match)}
\]
**The equation that matches the solution set {5} is**:
**\(x^2 - 10 = 15\)** (since it has a solution of \(x = 5\)).
---
**Question 2: What is the value of \(p\) in the following equation?**
Given:
\(20p - 3 = 5\)
To solve for \(p\):
\[
20p = 5 + 3 \\
20p = 8 \\
p = \frac{8}{20} \\
p = \frac{2}{5} \approx 0.4 \, \text{(not an option)}
\]
In the given options: 1, 3, 5, 7, none match our result. Please check if the equation provided is correct.
---
**Question 3: Which of the following equations has the solution set \(x = \{-95, 3\}\)?**
1. \((x - 3)(9x + 5) = 0\)
- Solutions: \(x = 3\) and \(9x + 5 = 0\) gives \(x = -\frac{5}{9}\) (not a match).
2. \(-3x(5x + 9) = 0\)
- Solutions: \(x = 0\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
3. \((x + 3)(9x - 5) = 0\)
- Solutions: \(x = -3\) and \(9x - 5 = 0\) gives \(x = \frac{5}{9}\) (not a match).
4. \((x - 3)(5x + 9) = 0\)
- Solutions: \(x = 3\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
**None of the above equations directly represent the solution set \(x = \{-95, 3\}\).** The equation that should represent this condition is:
\[
(x - 3)(x + 95) = 0
\]
This indicates that there may be an oversight in the provided options. Please recheck the equations again for correctness.