9.
Joe wants to fence a rectangular pen for his goats. the length of the pen should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?
I want to know if I am correct... This is my answer
y ≥ 60
2x + 2y ≤ 260
I've been waiting patiently for the past 10 mins... I need to know if this is correct or not please...
looks good
Okay, Thanks ^-^
Your answer is almost correct! However, there is a small mistake in the second inequality. Let me explain the correct solution for you.
Joe wants to fence a rectangular pen for his goats. Let's assume that the length of the pen is represented by 'x' and the width of the pen is represented by 'y'. Based on the given conditions, we can write the following inequalities:
1. The length of the pen should be at least 60 ft: x ≥ 60
This inequality ensures that the length of the pen is greater than or equal to 60 feet.
2. The distance around the pen should be no more than 260 ft: 2x + 2y ≤ 260
This inequality represents the perimeter of the rectangular pen. Since the perimeter is equal to the sum of all four sides of the rectangle, we get 2x + 2y. The sum should be less than or equal to 260 feet.
Combining these two inequalities, we get the system of inequalities:
x ≥ 60
2x + 2y ≤ 260
To graphically represent the possible dimensions, you can plot these inequalities on a coordinate plane. The x-axis represents the length of the pen and the y-axis represents the width of the pen. Shade the region that satisfies both inequalities, which will be the feasible region.
Please note that the inequalities provided assume the dimensions are positive values. If negative values or zero values of dimensions are applicable, the inequalities need to be adjusted accordingly.