A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet.
write a system of inequalities to represent this situation

2*x + 2*y ≤ 165 ft

x > 50ft

0ft < y ≤ 20ft

Step-by-step explanation:

For a rectangle with length x and width y, the perimeter of the triangle is:

P = 2*x + 2*y

The perimeter needs to be equal or smaller than the length of fencing that the farmer has, then:

2*x + 2*y ≤ 165 ft

We also know that:

(x strictly larger than 50ft)

x > 50ft

(y can be, at most, 20 ft)

0ft < y ≤ 20ft

(where we added the restriction that y needs to be larger than zero, because we can not have a width equal or smaller than zero)

Then the system of inequalities that represent this situation is:

2*x + 2*y ≤ 165 ft

x > 50ft

0ft < y ≤ 20ft

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: