Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.