Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A circular pond is modeled by the equation x^2 + y^2= 225. A bridge over the pond is modeled by a segment of the equation x – 7y = –75. What are the coordinates of the points where the bridge meets the edge of the pond?
A (9, 12) and (–12, 9)
B (9, 12) and (12, 9)
C (9, –12) and (–12, –9)
D (–9, 12) and (12, –9)


Sagot :

naǫ
[tex]x^2+y^2=225 \\ x-7y=-75 \\ \\ \hbox{solve the second equation for x:} \\ x-7y=-75 \ \ \ |+7y \\ x=7y-75 \\ \\ \hbox{substitute 7y-75 for x in the first equation:} \\ (7y-75)^2+y^2=225 \\ 49y^2-1050y+5625+y^2=225 \\ 50y^2-1050y+5625=225 \ \ \ \ \ \ \ \ \ |-225 \\ 50y^2-1050y+5400=0 \ \ \ \ \ \ \ \ \ \ \ \ |\div 50 \\ y^2-21y+108=0 \\ y^2-9y-12y+108=0 \\ y(y-9)-12(y-9)=0 \\ (y-12)(y-9)=0 \\ y-12=0 \ \lor \ y-9=0 \\ y=12 \ \lor \ y=9[/tex]

[tex]x=7y-75 \\ x=7 \times 12 -75 \ \lor \ x=7 \times 9-75 \\ x=84-75 \ \lor \ x=63-75 \\ x=9 \ \lor \ x=-12 \\ \\ (x,y)=(9,12) \hbox{ or } (x,y)=(-12,9)[/tex]

The points are (9,12) and (-12,9).
The answer is A.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.