AnswersAlgebra 2Systems of Inequalities — QuizQuestion 3
3
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Systems of Inequalities — Quiz

Question 3 • Algebra 2

A large garden has a set of underground sprinklers. Suppose the center of the garden is located at the origin of a grid with intervals measured in feet. One sprinkler is positioned at open paren 2 comma 4 close paren and reaches a radius of 8 feet. The second sprinkler is positioned at open paren negative 6 comma negative 4 close paren and reaches a radius of 6 feet. The system of inequalities represents this scenario. open parenthesis x minus 2 close parenthesis squared plus open parenthesis y minus 4 close parenthesis squared is less than or equal to 64; open parenthesis x plus 6 close parenthesis squared plus open parenthesis y plus 4 close parenthesis squared is less than or equal to 36 Which location is in the region for plants receiving the maximum amount of water?

Answer
A
open paren negative 7 comma 1 close paren
B
open paren 1 comma negative 5 close paren
C
open paren negative 3 comma negative 1 close paren
D
open paren 2 comma 1 close paren

Explanation

Plants receive the maximum amount of water where both sprinklers’ coverage regions overlap, so the point must satisfy both inequalities. At (−3, −1), the squared distance to (2, 4) is 5² + 5² = 50, which is at most 64. Its squared distance to (−6, −4) is 3² + 3² = 18, which is at most 36. Therefore, (−3, −1) is covered by both sprinklers.

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