To determine which statements are true regarding the solution for the width (w) of the rectangular run, let's first solve the equation based on the information given.
The equation representing the perimeter of the rectangle is: \[ 2l + 2w = 62 \]
Given that the length (l) is 20 feet, we can substitute this into the equation: \[ 2(20) + 2w = 62 \] \[ 40 + 2w = 62 \]
Next, we can isolate the term with the variable w: \[ 2w = 62 - 40 \] \[ 2w = 22 \]
Now, divide by 2 to solve for w: \[ w = 11 \]
Now, let's evaluate the statements based on our calculations:
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The value of w cannot be a negative number.
- True, since dimensions cannot be negative.
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Substitution is used to replace the variable l with a value of 20.
- True, this is exactly what we did in our calculations.
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The subtraction property of equality is used to isolate the term with the variable w.
- True, we subtracted 40 from both sides of the equation to isolate terms involving w.
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The value of w is 10 feet.
- False, as we calculated that w = 11 feet.
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The value of w can be 0.
- False, while mathematically it can be, it would not make sense for a width of a dog run.
Thus, the true statements are:
- The value of w cannot be a negative number.
- Substitution is used to replace the variable l with a value of 20.
- The subtraction property of equality is used to isolate the term with the variable w.