Solve the problem.
-A weak earthquake occurred roughly 4 km south and 5 km west of the center of Shelbyville. The quake could be felt 7 km away. Suppose the origin of the map is placed at the center of Shelbyville With the positive x-axis pointing east and the positive y-axis pointing north. Write an inequality that Describes the points on the map for which the earthquake could be felt, and determine whether the Quake could be felt at the center of Shelbyville.
A) $| x + 4 | + | y + 5 | \leq 7$; No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville.
B) $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49 ;$ No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville.
C) $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49$; Yes, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville.
D) $| x + 4 | + | y + 5 | \leq 7 ; \mathrm { Yes }$, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville.

Question

Solve the problem.
-A weak earthquake occurred roughly 4 km south and 5 km west of the center of Shelbyville. The quake could be felt 7 km away. Suppose the origin of the map is placed at the center of Shelbyville With the positive x-axis pointing east and the positive y-axis pointing north. Write an inequality that Describes the points on the map for which the earthquake could be felt, and determine whether the Quake could be felt at the center of Shelbyville. 
A) $| x + 4 | + | y + 5 | \leq 7$; No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville.
B) $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49 ;$ No, the quake was $9 \mathrm {~km}$ from the center of Shelbyville.
C) $( x + 4 ) ^ { 2 } + ( y + 5 ) ^ { 2 } \leq 49$; Yes, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville.
D) $| x + 4 | + | y + 5 | \leq 7 ; \mathrm { Yes }$, the quake was $6.4 \mathrm {~km}$ from the center of Shelbyville.

Quizplus · Accepted Answer

The correct inequality to describe the points on the map where the earthquake could be felt is a circle equation $(x + 4)^2 + (y + 5)^2 \leq 49$, because the earthquake's radius of effect is 7 km (hence, radius squared is $7^2 = 49$). The earthquake's epicenter is 4 km south and 5 km west of Shelbyville, so its coordinates relative to Shelbyville are (-4, -5). Using the distance formula, the distance from the center of Shelbyville to the earthquake's epicenter is $\sqrt{(-4)^2 + (-5)^2} = \sqrt{16 + 25} = \sqrt{41}$, which is approximately 6.4 km, indicating the quake could indeed be felt at the center of Shelbyville.

Solve the Problem ∣x+4∣+∣y+5∣≤7| x + 4 | + | y + 5 | \leq 7∣x+4∣+∣y+5∣≤7

Solve the Problem $| x + 4 | + | y + 5 | \leq 7$