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 truly need help on this, if you can, please show me how you got it so that I can finish the rest of the questions. Thanks ion advance!
Ohhhhh! So it's:
y ≥ 60
2x + 2y ≤ 260
Is that correct?
yup it is
P = 2L + 2W
260 > 2(60) + 2W
Thank You!
which graph is it? Y´all are confusing.
Oh, goat fencing! That sounds exciting. Let's solve this problem together and make it farm-tastic!
First, let's break down the problem:
Let's call the length of the pen L, and the width W.
We're given two conditions:
1. The length of the pen should be at least 60 ft, which we can write as L ≥ 60.
2. The distance around the pen (perimeter) should be no more than 260 ft, which we can write as 2L + 2W ≤ 260.
Now we can create our system of inequalities:
L ≥ 60
2L + 2W ≤ 260
To make it simpler, let's rearrange the perimeter inequality a bit:
2L ≤ 260 - 2W
L ≤ 130 - W
Now, let's graph these inequalities!
On a coordinate plane, draw the axes and label them. Let's put L on the x-axis and W on the y-axis.
For the first inequality, L ≥ 60, draw a horizontal line at L = 60, and shade everything above it, since we want L to be greater than or equal to 60.
For the second inequality, L ≤ 130 - W, draw the line L = 130 - W. Since it's a "less than or equal to" inequality, we'll draw a dashed line. I'll let you figure out the slope and intercept!
Now, we just need to shade the appropriate area. Since we want the values of L and W that satisfy both conditions, shade the region that is below the L = 60 line and below the L = 130 - W line.
Ta-da! That's your graph! Now you can determine the possible dimensions of the pen by looking at the shaded region.
I hope that helped, and remember, farm work can be a baa-ll of fun!
To determine the possible dimensions of the rectangular pen, we can set up a system of inequalities based on the given information.
Let's assume that the length of the rectangular pen is represented by 'L' and the width is represented by 'W'.
Since the length of the pen should be at least 60 ft, we can write the first inequality as:
L ≥ 60
The distance around the pen, which is the perimeter, should be no more than 260 ft. The formula for the perimeter of a rectangular shape is given by:
Perimeter = 2L + 2W
So, we can write the second inequality as:
2L + 2W ≤ 260
Now we have our system of inequalities:
L ≥ 60
2L + 2W ≤ 260
To graphically represent this system of inequalities, we can plot them on a coordinate plane.
First, graph the line L = 60. Since L is greater than or equal to 60, the line should be solid. This line represents the minimum length of 60 ft.
Next, graph the line 2L + 2W = 260. To do this, we can rewrite it in slope-intercept form (y = mx + b). Divide both sides by 2:
L + W = 130
Solving for W:
W = 130 - L
Now we have our slope-intercept form:
W = -L + 130
Plot this line on the graph, and draw it as a broken line since the inequality is less than or equal to. This line represents the combination of length and width that gives a perimeter of 260 ft.
The shaded region where both inequalities are true represents the possible dimensions of the rectangular pen.
I have provided a graphical representation of the system of inequalities for reference. Please note that the scale and units are not mentioned, so the graph is only an illustration and not an accurate representation of the dimensions.
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L W
In the shaded region, you can find the possible dimensions (length and width) of the rectangular pen that satisfy both inequalities.