Answer:
Step-by-step explanation:
C(3 , -2) & D (7, -8)
Distance = ![\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
![CD = \sqrt{(7-3)^{2}+(-8-(-2))^{2}}\\\\=\sqrt{(7-3)^{2}+(-8+2)^{2}}\\\\=\sqrt{(4)^{2}+(-6)^{2}}\\\\=\sqrt{16+36}\\\\=\sqrt{52}\\\\](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B%287-3%29%5E%7B2%7D%2B%28-8-%28-2%29%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%287-3%29%5E%7B2%7D%2B%28-8%2B2%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%284%29%5E%7B2%7D%2B%28-6%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B16%2B36%7D%5C%5C%5C%5C%3D%5Csqrt%7B52%7D%5C%5C%5C%5C)
≈ 7.2 units
We are given : Distance of the swing = 100 feet.
Distance of slide = 80 feet.
Angle between swing and slide = 30 degrees.
We need to find the distance between the swing and the slide.
Distance of swing, distance of slide and distance between the swing and the slide form a triangle.
We can apply cosine law to find the distance between the swing and the slide.
c^2 = a^2 +b^2 - 2ab cos C
c^2 = 100^2 +80^2 - 2(100)(80) cos 30°
c^2 = 10000 + 6400 -2* 8000 ![(\frac{\sqrt{3}} 2)}](https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%202%29%7D)
c^2 = 16400 - 8000![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
c^2 = 16400 - 13856
c^2 = 2544
![c =\sqrt{2544}](https://tex.z-dn.net/?f=c%20%3D%5Csqrt%7B2544%7D)
c= 50.44
c = 50 feet approximately.
<h3>Therefore, the approximate distance between the swing and the slide is 50 feet.</h3>
B. You can determine this by remember that the ordered pair is like a coordinate, the first digit represents the x and the second represents the y. Plug them in to both equations and if they work in both then it’s a solution, if it works in only one it is not.
Answer: 3 different ways
Those three ways, I'll label as A, B, and C
A) Buying the 78 cookies one at a time
B) Buying 6 packs of the 13-count cookies, so 13*6 = 78 cookies total.
C) Buying 2 packs of the 39-count cookies, so 2*39 = 78 cookies total
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For option A, we can imagine a rectangle that is 1 unit high and 78 units long giving an area of 1*78 = 78. Or we can imagine a single row of 78 cookies in this row.
In option B, we can have a rectangle that is 13 by 6, giving an area of 78. Or We could have 6 rows of 13 cookies per row (each row representing a package of cookies).
Option C would be similar to B, instead there would be 2 rows of 39 cookies per row.