Question
The Celsius to Fahrenheit formula: F = 9/5C + 32
Solve this formula for C. Check all answers that are true.
(4 points)
A. The Celsius to Fahrenheit formula: F=95C+32
Solve this formula for C. Check all answers that are true.
(4 points)
Responses
First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.
First step is to add 32 to both sides.
First step is to add 32 to both sides.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
First step is to add 32 to both sides.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
Solve this formula for C. Check all answers that are true.
(4 points)
A. The Celsius to Fahrenheit formula: F=95C+32
Solve this formula for C. Check all answers that are true.
(4 points)
Responses
First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.
First step is to add 32 to both sides.
First step is to add 32 to both sides.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
First step is to add 32 to both sides.
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5
Solution: 5/9F - 32 = C
To solve this equation for C, you would have to distribute at some point.
Answers
GPT-4o mini
To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5}C + 32 \) for \( C \), let's go through the steps.
1. **Start with the original equation**:
\( F = \frac{9}{5}C + 32 \)
2. **Subtract 32 from both sides**:
\( F - 32 = \frac{9}{5}C \)
3. **Multiply both sides by \( \frac{5}{9} \)** to isolate \( C \):
\( C = \frac{5}{9}(F - 32) \)
Which can also be written as:
\( C = \frac{5}{9}F - \frac{160}{9} \)
However, the expression \( C = \frac{5}{9}(F - 32) \) is the more common form to represent it.
### Checking the Given Responses
1. **First step is to multiply by 9 on each side.**
**False** - The first step involves subtracting 32, not multiplying.
2. **First step is to add 32 to both sides.**
**False** - You need to subtract 32 from both sides, not add.
3. **The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.**
**False** - The next step should be to multiply both sides by \( \frac{5}{9} \), not just 5.
4. **The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5.**
**False** - Dividing both sides by 5 does not isolate \( C \).
5. **Solution: \( \frac{5}{9}F - 32 = C \)**
**False** - This is not correct because it has \( -32 \) on the wrong side.
6. **To solve this equation for C, you would have to distribute at some point.**
**False** - The distribution is not necessary. You are simply calculating \( \frac{5}{9}(F - 32) \).
### Correct Solution
In summary, the correct answer (however not one of the provided options) should be:
**Solution: \( C = \frac{5}{9}(F - 32) \)**
None of the provided statements are true based on the correct steps needed to solve the equation.
1. **Start with the original equation**:
\( F = \frac{9}{5}C + 32 \)
2. **Subtract 32 from both sides**:
\( F - 32 = \frac{9}{5}C \)
3. **Multiply both sides by \( \frac{5}{9} \)** to isolate \( C \):
\( C = \frac{5}{9}(F - 32) \)
Which can also be written as:
\( C = \frac{5}{9}F - \frac{160}{9} \)
However, the expression \( C = \frac{5}{9}(F - 32) \) is the more common form to represent it.
### Checking the Given Responses
1. **First step is to multiply by 9 on each side.**
**False** - The first step involves subtracting 32, not multiplying.
2. **First step is to add 32 to both sides.**
**False** - You need to subtract 32 from both sides, not add.
3. **The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.**
**False** - The next step should be to multiply both sides by \( \frac{5}{9} \), not just 5.
4. **The next step from \( F - 32 = \frac{9}{5}C \), could be to divide both sides by 5.**
**False** - Dividing both sides by 5 does not isolate \( C \).
5. **Solution: \( \frac{5}{9}F - 32 = C \)**
**False** - This is not correct because it has \( -32 \) on the wrong side.
6. **To solve this equation for C, you would have to distribute at some point.**
**False** - The distribution is not necessary. You are simply calculating \( \frac{5}{9}(F - 32) \).
### Correct Solution
In summary, the correct answer (however not one of the provided options) should be:
**Solution: \( C = \frac{5}{9}(F - 32) \)**
None of the provided statements are true based on the correct steps needed to solve the equation.