Answer:
![\fbox{\begin{minipage}{11em}N is closer to P than M\end{minipage}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%7Bminipage%7D%7B11em%7DN%20is%20closer%20to%20P%20than%20M%5Cend%7Bminipage%7D%7D)
Step-by-step explanation:
<em>Step 1: Define the way to calculate distance between 2 points in two-dimensional (2D) plane</em>
Supposing that there are two points
and
on 2D plane.
The distance
between these two points is calculated by:
![d = \sqrt{(x_{1} - x_{2}) ^{2} + (y_{1} - y_{2})^{2} }](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_%7B1%7D%20-%20x_%7B2%7D%29%20%5E%7B2%7D%20%2B%20%20%28y_%7B1%7D%20-%20y_%7B2%7D%29%5E%7B2%7D%20%7D)
<em>Step 2: Calculate the distance </em>
<em>between </em>
<em> & </em>
<em> and distance </em>
<em>between </em>
<em> and </em>![P(-2, -1)](https://tex.z-dn.net/?f=P%28-2%2C%20-1%29)
Applying the formula in step 1:
![d_{1} = \sqrt{(3+ 2) ^{2} + (6 + 1)^{2} } = \sqrt{25 + 49} = \sqrt{74}](https://tex.z-dn.net/?f=d_%7B1%7D%20%3D%20%5Csqrt%7B%283%2B%202%29%20%5E%7B2%7D%20%2B%20%20%286%20%2B%201%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B25%20%2B%2049%7D%20%3D%20%5Csqrt%7B74%7D)
![d_{2} = \sqrt{(6+ 2) ^{2} + (-4 + 1)^{2} } = \sqrt{64 + 9} = \sqrt{73}](https://tex.z-dn.net/?f=d_%7B2%7D%20%3D%20%5Csqrt%7B%286%2B%202%29%20%5E%7B2%7D%20%2B%20%20%28-4%20%2B%201%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B64%20%2B%209%7D%20%3D%20%5Csqrt%7B73%7D)
<em>Step 3: Compare and conclude</em>
Because
=>
=> N is closer to P than M
Hope this helps!
:)
For a rectangle the opposite sides are parallel, which means the slope of opposite sides will be the same.
So,
Slope KL = Slope MN
Slope LM = Slope NK
Also two adjacent sides are perpendicular, so their slopes will be negative reciprocals of each other.
From the given points, we can find the slope of LM which will be:
![\frac{-2-(-4)}{3-1}= \frac{-2+4}{2} = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B-2-%28-4%29%7D%7B3-1%7D%3D%20%5Cfrac%7B-2%2B4%7D%7B2%7D%20%3D%201%20%20)
So,
Slope of LM = 1
Slope of NK = 1
Slope of KL = Slope of NK = -1
The answer is y= (x+3)^2 - 2
![y=2x+5\\y=1x+10\\\\y=2x+5=x+10\\x=5](https://tex.z-dn.net/?f=y%3D2x%2B5%5C%5Cy%3D1x%2B10%5C%5C%5C%5Cy%3D2x%2B5%3Dx%2B10%5C%5Cx%3D5)
The two equations are above. It is better to go to Ice Plex for skates under five hours and Skate World for skates over five hours.
The child is <u>59.4 inches tall</u>, assuming the length from the coach's shoulder to his head cap is approximately 10 inches.
<h3>What is Heigth?</h3>
Height refers to the vertical distance between the top and bottom of something.
Height measures the length of some objects or persons vertically to determine whether it is high or low, according to some ascertained criteria.
<h3>Data and Calculations:</h3>
Baseball coach's height = 70 inches
Coach's shoulder to head = 10.6 inches
Height of the child standing slightly below the coach's shoulder = 59.4 inches (70 - 10.6)
Thus, the child standing slightly below the coach's shoulder is 59.4 inches tall.
Learn more about height measurements at brainly.com/question/73194
#SPJ1
<h3>Question Completion:</h3>
Assume that the height of the coach from his shoulder to the head is 10.6 inches.