1. on saturday, mary goes to starbucks after soccer practice at the field and then the theatres to watch kpop demon hunters. what is the total distance that she traveled? round to three decimal places.
$d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$

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Accepted Answer

# Explanation:
## Step1: Find coordinates
Assume the coordinates of Field is $(x_1,y_1)=(-3,1)$, of AMC is $(x_2,y_2)=(5,5)$, and of Starbucks is $(x_3,y_3)=(-9,7)$.
## Step2: Calculate distance from Field to AMC
Use the distance formula $d=\sqrt{(y_2 - y_1)^2+(x_2 - x_1)^2}$.
Substitute $x_1=-3,y_1 = 1,x_2=5,y_2=5$ into the formula:
$$
\begin{align*}
d_{1}&=\sqrt{(5 - 1)^2+(5+ 3)^2}\
&=\sqrt{4^2+8^2}\
&=\sqrt{16 + 64}\
&=\sqrt{80}\
&=4\sqrt{5}\approx8.944
\end{align*}
$$
## Step3: Calculate distance from AMC to Starbucks
Substitute $x_2 = 5,y_2=5,x_3=-9,y_3=7$ into the distance formula:
$$
\begin{align*}
d_{2}&=\sqrt{(7 - 5)^2+(-9 - 5)^2}\
&=\sqrt{2^2+(-14)^2}\
&=\sqrt{4+196}\
&=\sqrt{200}\
&=10\sqrt{2}\approx14.142
\end{align*}
$$
## Step4: Calculate total distance
The total distance $d=d_{1}+d_{2}$.
$$
d\approx8.944 + 14.142=23.086
$$

# Answer:
$23.086$

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QUESTION IMAGE

Question

Explanation:

Step1: Find coordinates

Step2: Calculate distance from Field to AMC

Step3: Calculate distance from AMC to Starbucks

Step4: Calculate total distance

Answer: