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 angelas house to be (0, 0) on a coordinate grid. the system of inequalities represents this scenario.
{ ( x + 5 ) ^ { 2 } + ( y + 2 ) ^ { 2 } ≤ 144
( x - 8 ) ^ { 2 } + ( y - 7 ) ^ { 2 } ≤ 100
angela travels to a friends house, which is 4 miles east and 8 miles north of her house. will angela have cell phone service at her friends house?
angela will not have any cell phone service.
angela will have cell phone service from tower 1 only.
angela will have cell phone service from tower 2 only.
angela will have cell phone service from both towers.

Question

Accepted Answer

# Explanation:
## Step1: Substitute the coordinates of the friend's house $(4,8)$ into the first inequality $(x + 5)^{2}+(y + 2)^{2}\leq144$
Substitute $x = 4$ and $y=8$ into $(x + 5)^{2}+(y + 2)^{2}$:
$$
\begin{align*}
(4 + 5)^{2}+(8 + 2)^{2}&=9^{2}+10^{2}\
&=81 + 100\
&=181
\end{align*}
$$
Since $181>144$, the point $(4,8)$ does not satisfy the first inequality.

## Step2: Substitute the coordinates of the friend's house $(4,8)$ into the second inequality $(x - 8)^{2}+(y - 7)^{2}\leq100$
Substitute $x = 4$ and $y = 8$ into $(x - 8)^{2}+(y - 7)^{2}$:
$$
\begin{align*}
(4-8)^{2}+(8 - 7)^{2}&=(-4)^{2}+1^{2}\
&=16+1\
&=17
\end{align*}
$$
Since $17\leq100$, the point $(4,8)$ satisfies the second inequality.

# Answer:
Angela will have cell phone service from tower 2 only.

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Question

Explanation:

Step1: Substitute the coordinates of the friend's house \((4,8)\) into the first inequality \((x + 5)^{2}+(y + 2)^{2}\leq144\)

Step2: Substitute the coordinates of the friend's house \((4,8)\) into the second inequality \((x - 8)^{2}+(y - 7)^{2}\leq100\)

Answer: