Question
What is the first step of solving cos(42)=18x
?
(1 point)
Responses
multiply both sides by 18
multiply both sides by 18
divide both sides by 18
divide both sides by 18
divide both sides by x
divide both sides by x
multiply both sides by x
multiply both sides by x
Question 2
What is the second step?(1 point)
Responses
divide both sides by the cos(42)
divide both sides by the cos(42)
multiply both sides by cos(42)
multiply both sides by cos(42)
divide both sides by x
divide both sides by x
divide both sides by 42
divide both sides by 42
x is by itself, so you put the other side of the equation in your calculator
x is by itself, so you put the other side of the equation in your calculator
Question 3
What answer do you get after you complete the problem solving for x?Round to 1 decimal place
(1 point)
x =
?
(1 point)
Responses
multiply both sides by 18
multiply both sides by 18
divide both sides by 18
divide both sides by 18
divide both sides by x
divide both sides by x
multiply both sides by x
multiply both sides by x
Question 2
What is the second step?(1 point)
Responses
divide both sides by the cos(42)
divide both sides by the cos(42)
multiply both sides by cos(42)
multiply both sides by cos(42)
divide both sides by x
divide both sides by x
divide both sides by 42
divide both sides by 42
x is by itself, so you put the other side of the equation in your calculator
x is by itself, so you put the other side of the equation in your calculator
Question 3
What answer do you get after you complete the problem solving for x?Round to 1 decimal place
(1 point)
x =
Answers
GPT-4o mini
To solve the equation \( \cos(42) = 18x \), let's break down each question:
### Question 1: First Step
The first step in solving the equation \( \cos(42) = 18x \) would be to isolate \( x \). To do this, you would want to divide both sides by 18.
**Correct Response:**
- **divide both sides by 18**
### Question 2: Second Step
After dividing both sides of the equation by 18, you would arrive at:
\[
x = \frac{\cos(42)}{18}
\]
The second step to isolate \( x \) would be to handle \( \cos(42) \). Since \( \cos(42) \) is a constant, to solve for \( x \), you can simply input this value into your calculator.
So the most appropriate next step would be:
**Correct Response:**
- **x is by itself, so you put the other side of the equation in your calculator**
### Question 3: Final Calculation
Now, we need to calculate \( x \):
1. First, calculate \( \cos(42^\circ) \):
\[
\cos(42^\circ) \approx 0.7431 \quad (\text{approximately})
\]
2. Now divide this result by 18:
\[
x \approx \frac{0.7431}{18} \approx 0.0413
\]
3. Finally, rounding to one decimal place:
\[
x \approx 0.0
\]
(Since 0.0413 rounded to one decimal place is 0.0).
Thus, for the final response:
**Answer:**
- \( x \approx 0.0 \)
Let me know if you need further assistance!
### Question 1: First Step
The first step in solving the equation \( \cos(42) = 18x \) would be to isolate \( x \). To do this, you would want to divide both sides by 18.
**Correct Response:**
- **divide both sides by 18**
### Question 2: Second Step
After dividing both sides of the equation by 18, you would arrive at:
\[
x = \frac{\cos(42)}{18}
\]
The second step to isolate \( x \) would be to handle \( \cos(42) \). Since \( \cos(42) \) is a constant, to solve for \( x \), you can simply input this value into your calculator.
So the most appropriate next step would be:
**Correct Response:**
- **x is by itself, so you put the other side of the equation in your calculator**
### Question 3: Final Calculation
Now, we need to calculate \( x \):
1. First, calculate \( \cos(42^\circ) \):
\[
\cos(42^\circ) \approx 0.7431 \quad (\text{approximately})
\]
2. Now divide this result by 18:
\[
x \approx \frac{0.7431}{18} \approx 0.0413
\]
3. Finally, rounding to one decimal place:
\[
x \approx 0.0
\]
(Since 0.0413 rounded to one decimal place is 0.0).
Thus, for the final response:
**Answer:**
- \( x \approx 0.0 \)
Let me know if you need further assistance!