Respuesta :
The correct option is D. the number of sweatshirts for which cost and income are equal.
What is quadratic equation?
Any equation that contains only one element which squares the variable and none that raises it to a higher power.
The general form form of quadratic equation is-
ax² + bx + c = 0
According to the question;
Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.
- The money made by selling sweatshirts is represented by y in the systems of equations' first equation.
- The cost of producing x sweatshirts featuring team logos for the a professional sport league is represented by y in the second equation.
Step 1: Write the following system of equations as the first step.
[tex]\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}[/tex]
Step 2: Replace the value of "y" in the equation (2).
[tex]35 x=-0.05(x-400)^{2}+9492[/tex]
Step 3: Make the equation above simpler.
[tex]35 x=-0.05 x^{2}-8000+40 x+9492[/tex]
Step 4: Write the preceding equation in generalised quadratic form.
[tex]0.05 x^{2}-5 x-1492=0[/tex]
The processes above lead to the conclusion that option D provides the proper statement.
To know more about solution of a quadratic equation, here
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The complete question is-
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. What does the solution of the system represent in this context?
y=35x
y=-0.05(x-400)^2+9,492
A. the number of sweatshirts that generate the maximum income
B. the number of sweatshirts that generate the minimum cost
C. the number of sweatshirts for which the difference between cost and income is greatest.
D. the number of sweatshirts for which cost and income are equal
