Acircle is described by the equation (x−1/2 )^2 +(y−3/2 )^2 =4/9 . what are the cordinates for the center of the circle and the length of the radius? a) (-1/2 ,-3/2 ) , 2/3 units b) (-1/2 ,-3/2 ) , 4/9 units c) (1/2 ,3/2 ) , 4/9 units d) (1/2 ,3/2 ) , 2/3 units

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints