Respuesta :
For this, we are going to use both equations to find the intersection point on both of them. We got:
[tex]\begin{gathered} y=x^2-17x+89 \\ \text{and} \\ y=17x+25 \\ \Rightarrow x^2-17x+89=17x+25 \\ \Rightarrow x^2-17x+89-17x-25=0 \\ \Rightarrow x^2-34x+64=0 \end{gathered}[/tex]Finally, we find the roots of the polynomial to get the values of x that we need:
[tex]\begin{gathered} x^2-34x+64=0^{} \\ \Rightarrow(x-32)(x-2)=0 \end{gathered}[/tex]From this, we can see that the roots are x=2 and x=32, therefore, the sales will match on weeks 2 and 32.
Now, to calculate the sales, we use both values of x that we found to get the value of y in both equations:
For x = 2:
[tex]\begin{gathered} y=(2)^2-17(2)+89 \\ \Rightarrow y=4-34+89=59 \end{gathered}[/tex]For x=32:
[tex]\begin{gathered} y=(32)^2-17(32)+89 \\ \Rightarrow y=1024-544+89=569 \end{gathered}[/tex]Therefore, the sales on weeks 2 and 32 are 59 and 569 respectively.
