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Answer :
Let's solve the problems step by step.
### Part 1: Convert 87 kilograms to pounds
To convert kilograms to pounds, you can use the given conversion rate: 1 pound is approximately 0.45 kilograms.
1. Set up the conversion calculation:
[tex]\[
\text{Weight in pounds} = \frac{\text{Weight in kilograms}}{0.45}
\][/tex]
2. Plug the given weight in kilograms into the calculation:
[tex]\[
\text{Weight in pounds} = \frac{87}{0.45} \approx 193.33
\][/tex]
3. Round to the nearest whole number:
[tex]\[
\text{Rounded weight in pounds} = 193
\][/tex]
So, the person's weight in pounds is approximately 193 lb. Therefore, the answer is D. 193 lb.
### Part 2: Solve for [tex]\( x \)[/tex] in the equation [tex]\( y - y_1 = m(x - x_1) \)[/tex]
To solve for [tex]\( x \)[/tex], follow these steps:
1. Start with the equation:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
2. Distribute [tex]\( m \)[/tex] on the right side:
[tex]\[
y - y_1 = mx - mx_1
\][/tex]
3. Add [tex]\( mx_1 \)[/tex] to both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
y - y_1 + mx_1 = mx
\][/tex]
4. To solve for [tex]\( x \)[/tex], divide every term by [tex]\( m \)[/tex]:
[tex]\[
x = \frac{y - y_1 + mx_1}{m}
\][/tex]
5. Simplify the expression:
[tex]\[
x = \frac{y - y_1}{m} + x_1
\][/tex]
This matches option B: [tex]\( x = \frac{y-y_1}{m} + x_1 \)[/tex]. So the correct answer is B.
### Part 1: Convert 87 kilograms to pounds
To convert kilograms to pounds, you can use the given conversion rate: 1 pound is approximately 0.45 kilograms.
1. Set up the conversion calculation:
[tex]\[
\text{Weight in pounds} = \frac{\text{Weight in kilograms}}{0.45}
\][/tex]
2. Plug the given weight in kilograms into the calculation:
[tex]\[
\text{Weight in pounds} = \frac{87}{0.45} \approx 193.33
\][/tex]
3. Round to the nearest whole number:
[tex]\[
\text{Rounded weight in pounds} = 193
\][/tex]
So, the person's weight in pounds is approximately 193 lb. Therefore, the answer is D. 193 lb.
### Part 2: Solve for [tex]\( x \)[/tex] in the equation [tex]\( y - y_1 = m(x - x_1) \)[/tex]
To solve for [tex]\( x \)[/tex], follow these steps:
1. Start with the equation:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
2. Distribute [tex]\( m \)[/tex] on the right side:
[tex]\[
y - y_1 = mx - mx_1
\][/tex]
3. Add [tex]\( mx_1 \)[/tex] to both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[
y - y_1 + mx_1 = mx
\][/tex]
4. To solve for [tex]\( x \)[/tex], divide every term by [tex]\( m \)[/tex]:
[tex]\[
x = \frac{y - y_1 + mx_1}{m}
\][/tex]
5. Simplify the expression:
[tex]\[
x = \frac{y - y_1}{m} + x_1
\][/tex]
This matches option B: [tex]\( x = \frac{y-y_1}{m} + x_1 \)[/tex]. So the correct answer is B.
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