Each of the four inequalities given below defines a region in the xy plane. One of these four regions does nothave the following property. For any two points `(x_1,y_2) and (y_1,y_2)` in the region the piont `((x_1+x_2)/2*(y_1+y_2)/2)` is also in the region. The inequality defining this region is

Each of the four inequalities given below defines a region in the xy plane. One of these four regions does not have the following property. For any two points (x_1,y_1) and (x_2,y_2) in the region the point ((x_1+x_2)/2*(y_1+y_2)/2) is also in the region. The inequality defining this region is (1) x^2 + 2y^2 ≤ 1 (2)Max {|x| , | y| ≤ 1 (3) x^2 – y^2 ≤ 1 (4) y^2 – x ≤ 0

Shade the region given by inequality 2x + y ge 6

A region in the x-y plane is bounded by the curve y=sqrt(25-x^2) and the line y=0 . If the point (a ,a+1) lies in the interior of the region, then

Find the area of the region {(x,y): x^(2)+y^(2) le 1 le x + y}

The optimal solution of an L.P.P. occurs at two distinct points (x_1,y_1) and (x_2,y_2) of the feasible region. Will this solution occur at some other point also.

Sketch the curves and identity the region bunded by y=1nx, and y=2^(x). Find the area of this region.

Determine the region in the plane determined by the inequalities. y ge 2x, -2x + 3y le 6.

Determine the region in the plane determined by the inequalities y ge 2x and -2x + 3y le 6 .