Respuesta :
Answer:
The number of sweatshirts for which cost and income are equal
Step-by-step explanation:
Let y₁ represent the revenue from selling "x" sweatshirts and y₂ represent the cost of producing "x" sweatshirts, solving the system:
[tex]y_1=35x\\y_2=-0.05(x-400)^2+9,492\\y_1=y_2\\35x=-0.05(x-400)^2+9,492\\-0.05(x-400)^2-35x+9,492=0[/tex]
The solution of the equation above yields the number of sweatshirts for which the cost of production (y₂ ) is equal to the revenue from sales (y₁).
Therefore, the solution represents the number of sweatshirts for which cost and income are equal .
The number of sweatshirts for which cost and income are equal and this can be determined by using the substitution method.
Given :
- In the first equation in the system of equations, y represents the money collected from selling sweatshirts.
- In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
The following steps can be used in order to determine the solution of the system of the equation:
Step 1 - Write the given system of equations.
[tex]y = 35x[/tex] ---- (1)
[tex]y = -0.05(x - 400)^2+9492[/tex] ---- (2)
Step 2 - Now, substitute the value of 'y' in equation (2).
[tex]35x = -0.05(x - 400)^2+9492[/tex]
Step 3 - Simplify the above equation.
[tex]35x = -0.05x^2-8000+40x+9492[/tex]
Step 4 - Now, write the above equation in generalized quadratic form.
[tex]0.05x^2-5x-1492=0[/tex]
From the above steps, it can be concluded that the correct statement is given by option D).
For more information, refer to the link given below:
https://brainly.com/question/11897796
