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

the data in the table represents a companys 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 companys 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 $y = 196.2x-18710$: $y=196.2\times100 - 18710=19620 - 18710 = 910$ (far - off)

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 $y = 196.2x-18710$: $y=196.2\times200 - 18710=39240 - 18710 = 20530$ (far - off)

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 $y = 196.2x-18710$: $y=196.2\times300 - 18710=58860 - 18710 = 40150$ (far - off)

Step4: Compare the results with the table values

By substituting more values of x from the table into the equations, we find that the equation $y=-1.036x^{2}+1024.771x - 163710$ gives values that are closest to the values in the profit - based on - number - of - items - produced table.

Answer:

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