the data in the table represents a company’s profit based on the number of items produced.\nprofit based on…

the data in the table represents a company’s profit based on the number of items produced.\nprofit based on number of items produced\n| items produced (x) | dollars of profit (y) |\n| ---- | ---- |\n| 100 | -70,500 |\n| 200 | 50 |\n| 300 | 50,100 |\n| 400 | 80,300 |\n| 500 | 90,400 |\n| 600 | 78,000 |\nwhich equation best represents the data?\n○ y = -1.026x² + 1016.402x - 162075\n○ y = -1.036x² + 1024.771x - 163710\n○ y = 298.214x - 66317.667\n○ y = 196.2x - 18710

the data in the table represents a company’s profit based on the number of items produced.\nprofit based on number of items produced\n| items produced (x) | dollars of profit (y) |\n| ---- | ---- |\n| 100 | -70,500 |\n| 200 | 50 |\n| 300 | 50,100 |\n| 400 | 80,300 |\n| 500 | 90,400 |\n| 600 | 78,000 |\nwhich equation best represents the data?\n○ y = -1.026x² + 1016.402x - 162075\n○ y = -1.036x² + 1024.771x - 163710\n○ y = 298.214x - 66317.667\n○ y = 196.2x - 18710

Answer

Explanation:

Step1: Substitute (x = 100) into each equation

For (y=-1.026x^{2}+1016.402x - 162075):

[y=-1.026\times(100)^{2}+1016.402\times100 - 162075] [y=-10260+101640.2 - 162075=-70494.8]

For (y=-1.036x^{2}+1024.771x - 163710):

[y=-1.036\times(100)^{2}+1024.771\times100 - 163710] [y=-10360+102477.1 - 163710=-71592.9]

For (y = 298.214x-66317.667):

[y=298.214\times100-66317.667=29821.4 - 66317.667=-36496.267]

For (y = 196.2x-18710):

[y=196.2\times100-18710=19620 - 18710 = 910]

Step2: Substitute (x = 200) into each equation

For (y=-1.026x^{2}+1016.402x - 162075):

[y=-1.026\times(200)^{2}+1016.402\times200 - 162075] [y=- 41040+203280.4 - 162075 = 10165.4]

For (y=-1.036x^{2}+1024.771x - 163710):

[y=-1.036\times(200)^{2}+1024.771\times200 - 163710] [y=-41440+204954.2 - 163710 = -396.8]

For (y = 298.214x-66317.667):

[y=298.214\times200-66317.667=59642.8 - 66317.667=-6674.867]

For (y = 196.2x-18710):

[y=196.2\times200-18710=39240 - 18710 = 20530]

Step3: Substitute (x = 300) into each equation

For (y=-1.026x^{2}+1016.402x - 162075):

[y=-1.026\times(300)^{2}+1016.402\times300 - 162075] [y=-92340+304920.6 - 162075 = 50505.6]

For (y=-1.036x^{2}+1024.771x - 163710):

[y=-1.036\times(300)^{2}+1024.771\times300 - 163710] [y=-93240+307431.3 - 163710 = 50481.3]

For (y = 298.214x-66317.667):

[y=298.214\times300-66317.667=89464.2 - 66317.667 = 23146.533]

For (y = 196.2x-18710):

[y=196.2\times300-18710=58860 - 18710 = 40150]

Step4: Compare the results with the table values

By comparing the calculated (y) - values with the values in the table for different (x) - values, we find that the equation (y=-1.036x^{2}+1024.771x - 163710) gives values that are closest to the actual profit values in the table.

Answer:

(y=-1.036x^{2}+1024.771x - 163710)