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

question 104

Multiple Choice

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.

---

Definitions:

Oculus

A round or eye-like opening in a structure, often at the apex of a dome, letting light or air inside.

Dome

An architectural element resembling the upper half of a sphere, often used to cover a large space without internal supports, symbolizing the heavens or the sky in religious buildings.

Peristyle

In classical architecture, a colonnade all around the cella and its porch(es). A peripteral colonnade consists of a single row of columns on all sides; a dipteral colonnade has a double row all around.

Split

A city in Croatia known for its ancient ruins, particularly the Diocletian's Palace, and its beautiful Adriatic coastal location.