shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. she decides to…

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? check all that apply. the value of w is 10 feet. the value of w can be zero. 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.

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? check all that apply. the value of w is 10 feet. the value of w can be zero. 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.

Answer

Answer:

  • C. The value of (w) cannot be a negative number.
  • D. Substitution is used to replace the variable (l) with a value of 20.
  • E. The subtraction property of equality is used to isolate the term with the variable (w).

Explanation:

Step1: Analyze perimeter formula

The perimeter of a rectangle is (P = 2l+2w). Given (P = 62) and (l = 20), we have (62=2\times20 + 2w).

Step2: Analyze non - negativity of width

Width (w) represents a physical dimension, so (w\geq0), it can't be negative.

Step3: Analyze substitution

We substitute (l = 20) into the perimeter formula (2l + 2w=62).

Step4: Analyze solving for (w)

Starting with (62=40 + 2w), we use the subtraction property of equality. Subtract 40 from both sides: (62-40=40 + 2w-40), which simplifies to (22 = 2w).