Consider a linear programming problem in standard form, described in terms of the following initial tableau: δ3γξ β010α103 2 0 0 1 −2 2 η −1 3 1 0 0 0 −1 2 1 the entries matrix corresponding to having x2, x3, and x1 (in that order) be the basic variables. for each one of the following statements, find the ranges of values of the various parameters that will make the statement to be true. (a) (1 point) phase ii of the simplex method can be applied using this as an initial tableau. (b) (1 point) the first row in the present tableau (below the row with the reduced costs) indicates that the problem is infeasible. (c) (1 point) the corresponding basic solution is feasible, but we do not have an optimal basis. (d) (1 point) the corresponding basic solution is feasible and the first simplex iteration indicates that the optimal cost is −[infinity]. (e) (1 point) the corresponding basic solution is feasible, x6 is a candidate for entering the basis, and when x6 is the entering variable, x3 leaves the basis. (f) (1 point) the corresponding basic solution is feasible, x7 is a candidate for entering the basis, but if it does, the solution and the objective value remain unchanged.

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:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).