AnswersAlgebra 2Systems — TestQuestion 20
20
QuizMultiple Choice

Systems — Test

Question 20 • Algebra 2

A farm irrigation system waters a large field. Consider the center of the field as the origin and the rest of the field as a grid measured in yards. The first irrigation unit is located at the point open paren negative 400 comma negative 200 close paren and waters 500 yards in every direction. The second is located at open paren 200 comma 300 close paren and waters 400 yards in every direction. The system of inequalities represents this scenario. open parenthesis x plus 400 close parenthesis squared plus open parenthesis y plus 200 close parenthesis squared is less than or equal to 250,000; open parenthesis x minus 200 close parenthesis squared plus open parenthesis y minus 300 close parenthesis squared is less than or equal to 160,000 Crops watered by both systems will most likely grow more quickly. Which location will receive the maximum amount of water?

Answer
A
open paren 100 comma 100 close paren
B
open paren negative 100 comma 100 close paren
C
open paren 100 comma negative 100 close paren
D
open paren negative 100 comma negative 100 close paren

Explanation

A location receives water from both systems if it lies within both circles. For choice B, (−100, 100), the squared distance to the first unit at (−400, −200) is 300² + 300² = 180,000, which is at most 250,000. Its squared distance to the second unit at (200, 300) is 300² + 200² = 130,000, which is at most 160,000. So choice B, (−100, 100), is watered by both systems; the other choices do not meet both inequalities.

AI-written and checked against the verified answer.

Previous
Next

More from this Course

Quiz
25 verified answers

Test

practice test
12 verified answers

Practice Test

practice test
16 verified answers

Practice Test