5
QuizMultiple Choice

Systems of Inequalities — Quiz

Question 5 • Algebra 2

Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be open paren 0 comma 0 close paren on a coordinate grid. The system of inequalities represents this scenario. open parenthesis x plus 5 close parenthesis squared plus open parenthesis y plus 2 close parenthesis squared is less than or equal to 144; open parenthesis x minus 8 close parenthesis squared plus open parenthesis y minus 7 close parenthesis squared is less than or equal to 100 Angela travels to a friend’s house, which is 4 miles east and 8 miles north of her house. Will Angela have cell phone service at her friend’s house?

Answer
A
Angela will not have any cell phone service.
B
Angela will have cell phone service from both towers.
C
Angela will have cell phone service from tower 2 only.
D
Angela will have cell phone service from tower 1 only.

Explanation

Angela’s friend’s house is at (4, 8). Its squared distance from Tower 1 is (4 + 5)² + (8 + 2)² = 181, which is greater than 144, so it is outside Tower 1’s coverage. Its squared distance from Tower 2 is (4 − 8)² + (8 − 7)² = 17, which is at most 100, so Angela will have service from Tower 2 only.

AI-written and checked against the verified answer.

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