An automobile tire manufacturer collected the data in the table relating tire pressure x​ (in pounds per square​ inch) and mileage​ (in thousands of​ miles). A mathematical model for the data is given by ​f(x)=−0.554x2+35.5x−514. Answer parts​ (A) through​ (D) below. x Mileage 28 45 30 51 32 56 34 50 36 46 ​(A) Complete the table below.   x Mileage f(x) 28 45   30 51   32 56   34 50   36 46   ​(Round to one decimal place as​ needed.) A.         20602060xf(x)         A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.   B.         20602060xf(x)         A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.   C.         20602060xf(x)         A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.   D.         20602060xf(x)         A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.   ​(C) Use the modeling function​ f(x) to estimate the mileage for a tire pressure of 29 ​lbs/sq in. and for 35 ​lbs/sq in.   The mileage for the tire pressure 29 ​lbs/sq in. is     The mileage for the tire pressure 35 ​lbs/sq in. is     .​(Round to two decimal places as​ needed.)   ​(D) Write a brief description of the relationship between tire pressure and mileage.     A. As tire pressure​ increases, mileage decreases to a minimum at a certain tire​ pressure, then begins to increase.   B. As tire pressure​ increases, mileage decreases.   C. As tire pressure​ increases, mileage increases to a maximum at a certain tire​ pressure, then begins to decrease.   D. As tire pressure​ increases, mileage increases

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.