Question
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2l+2w=62
to find the width of the run. Which statements are true of the solution? Select the three that apply.(3 points)
Responses
The subtraction property of equality is used to isolate the term with the variable w.
The subtraction property of equality is used to isolate the term with the variable w.
The value of w is 10 feet.
The value of w is 10 feet.
The value of w cannot be a negative number.
The value of w cannot be a negative number.
The value of w can be 0.
The value of w can be 0.
Substitution is used to replace the variable l with a value of 20.
to find the width of the run. Which statements are true of the solution? Select the three that apply.(3 points)
Responses
The subtraction property of equality is used to isolate the term with the variable w.
The subtraction property of equality is used to isolate the term with the variable w.
The value of w is 10 feet.
The value of w is 10 feet.
The value of w cannot be a negative number.
The value of w cannot be a negative number.
The value of w can be 0.
The value of w can be 0.
Substitution is used to replace the variable l with a value of 20.
Answers
GPT-4o mini
To solve for the width \( w \) of the rectangular run given that the perimeter is 62 feet and the length \( l \) is 20 feet, Shana starts with the equation:
\[ 2l + 2w = 62. \]
Substituting \( l = 20 \):
\[ 2(20) + 2w = 62, \]
\[ 40 + 2w = 62. \]
Next, we isolate \( 2w \) by subtracting 40 from both sides:
\[ 2w = 62 - 40, \]
\[ 2w = 22. \]
Now, dividing both sides by 2:
\[ w = 11. \]
1. **The subtraction property of equality is used to isolate the term with the variable w.** - This statement is **true** because we subtracted 40 from both sides of the equation.
2. **The value of w is 10 feet.** - This statement is **false** because the value of \( w \) calculated is 11 feet, not 10.
3. **The value of w cannot be a negative number.** - This statement is **true** since a width \( w \) in this context cannot be negative.
4. **The value of w can be 0.** - This statement is **false** because if \( w \) were 0, the run wouldn't have a width.
5. **Substitution is used to replace the variable l with a value of 20.** - This statement is **true** since we substituted \( l \) with 20 in the equation.
Based on this analysis, the three true statements are:
1. The subtraction property of equality is used to isolate the term with the variable w.
2. The value of w cannot be a negative number.
3. Substitution is used to replace the variable l with a value of 20.
\[ 2l + 2w = 62. \]
Substituting \( l = 20 \):
\[ 2(20) + 2w = 62, \]
\[ 40 + 2w = 62. \]
Next, we isolate \( 2w \) by subtracting 40 from both sides:
\[ 2w = 62 - 40, \]
\[ 2w = 22. \]
Now, dividing both sides by 2:
\[ w = 11. \]
1. **The subtraction property of equality is used to isolate the term with the variable w.** - This statement is **true** because we subtracted 40 from both sides of the equation.
2. **The value of w is 10 feet.** - This statement is **false** because the value of \( w \) calculated is 11 feet, not 10.
3. **The value of w cannot be a negative number.** - This statement is **true** since a width \( w \) in this context cannot be negative.
4. **The value of w can be 0.** - This statement is **false** because if \( w \) were 0, the run wouldn't have a width.
5. **Substitution is used to replace the variable l with a value of 20.** - This statement is **true** since we substituted \( l \) with 20 in the equation.
Based on this analysis, the three true statements are:
1. The subtraction property of equality is used to isolate the term with the variable w.
2. The value of w cannot be a negative number.
3. Substitution is used to replace the variable l with a value of 20.