select the correct answer. a company manufactures school desks. the table shows the number of units that the…

select the correct answer. a company manufactures school desks. the table shows the number of units that the company sold each month over a nine - month period beginning in january. month, x 1 2 3 4 5 6 7 8 9 units, y 800 500 400 300 200 300 450 600 800 which equation best models the situation? o a. y = 7x + 450 o b. y = -7x + 450 o c. y = 34x² - 334x + 1,075 o d. y = -34x² + 334x + 1,075 reset next

select the correct answer. a company manufactures school desks. the table shows the number of units that the company sold each month over a nine - month period beginning in january. month, x 1 2 3 4 5 6 7 8 9 units, y 800 500 400 300 200 300 450 600 800 which equation best models the situation? o a. y = 7x + 450 o b. y = -7x + 450 o c. y = 34x² - 334x + 1,075 o d. y = -34x² + 334x + 1,075 reset next

Answer

Explanation:

Step1: Test option A with x = 1

When (x = 1), (y=7\times1 + 450=457\neq800).

Step2: Test option B with x = 1

When (x = 1), (y=-7\times1 + 450 = 443\neq800).

Step3: Test option C with x = 1

When (x = 1), (y=34\times1^{2}-334\times1 + 1075=34 - 334+1075 = 775\neq800).

Step4: Test option D with x = 1

When (x = 1), (y=-34\times1^{2}+334\times1 + 1075=-34 + 334+1075=1375\neq800). Let's use a more systematic approach of substituting multiple - points. We can use the general form of a quadratic regression (y = ax^{2}+bx + c). We have the system of equations using the points ((1,800)), ((2,500)), ((3,400)): For ((1,800)): (a\times1^{2}+b\times1 + c=800), i.e., (a + b + c=800) For ((2,500)): (a\times2^{2}+b\times2 + c=500), i.e., (4a+2b + c=500) For ((3,400)): (a\times3^{2}+b\times3 + c=400), i.e., (9a + 3b + c=400) Subtract the first equation from the second: ((4a + 2b + c)-(a + b + c)=500 - 800), (3a + b=-300) Subtract the second equation from the third: ((9a+3b + c)-(4a + 2b + c)=400 - 500), (5a + b=-100) Subtract the new - obtained first equation from the second: ((5a + b)-(3a + b)=-100+300), (2a = 200), (a=-34) Substitute (a=-34) into (3a + b=-300), (3\times(-34)+b=-300), (-102 + b=-300), (b = 334) Substitute (a=-34) and (b = 334) into (a + b + c=800), (-34+334 + c=800), (c = 1075) So the equation is (y=-34x^{2}+334x + 1075)

Answer:

D. (y=-34x^{2}+334x + 1075)