ANSWER
5.5
EXPLANATION
We can use the cosine rule to find the missing side length.
The cosine rule is given as;
![{a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos( A)](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bc%7D%5E%7B2%7D%20%20-%202bc%20%5Ccos%28%20A%29%20)
Let the missing side be "a".
Then,
![{a}^{2} = {9}^{2} + {6}^{2} - 2 \times 9 \times 6 \cos(37 \degree)](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%7B9%7D%5E%7B2%7D%20%20%2B%20%20%7B6%7D%5E%7B2%7D%20%20-%202%20%5Ctimes%209%20%5Ctimes%206%20%5Ccos%2837%20%5Cdegree%29%20)
![{a}^{2} = 81+ 36- 86.253](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%2081%2B%20%2036-%2086.253)
![{a}^{2} = 30.74736](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%2030.74736)
![a = \sqrt{30.747}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B30.747%7D%20)
![a \approx5.5](https://tex.z-dn.net/?f=a%20%5Capprox5.5)
Therefore the missing side length is approximately 5.5 units to the nearest tenth.
Answer:
Phone 1 will allow Ellie to talk the longest
Step-by-step explanation:
Phone 1:
(0.10x) + 6 = y
(0.10x) + 6 - 6 = 22 - 6
0.10/0.10x = 16/0.10
x = <u>160</u> minutes
Phone 2:
(0.25x) + 5 = y
(0.25x) + 5 - 5 = 22 - 5
0.25/0.25x = 17/0.25
x = <u>68</u> minutes
Move the 3 to right side of the equation and it becomes -3 as u r subtracting 3 from both sides and u should get x = -8 - 3, x = -11. Idk what u mean by pullout tho
Answer:
MO = 8 units
MP = 4 units
Step-by-step explanation:
![In\: \triangle MOP, \\\angle P = 90\degree ... (given) \\\angle M = 60\degree ... (given) \\\therefore \angle O = 30\degree(3^{rd} \: \angle \: of\: \triangle) \\Let \huge\purple {MO = x \: units}... (1)\\\therefore MP = \frac{1}{2} \times MO\\(side\: opposite \: to\: 30\degree) \\\\\therefore MP = \frac{1}{2} \times x\\\\\huge\red {\therefore MP = \frac{1}{2} x}.... (2)\\\\\therefore PO = \frac{\sqrt 3}{2} \times MO\\(side\: opposite \: to\: 60\degree) \\\\\therefore PO = \frac{\sqrt 3}{2} \times x\\\\\huge\orange{\therefore PO = \frac{\sqrt 3}{2}x} \\\\\because MP + PO + MO = P(\triangle MOP) \\\\\therefore \frac{1}{2} x+\frac{\sqrt 3}{2}x+ x = 12+4\sqrt 3\\\\\therefore \frac{1}{2} x+x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\\therefore \frac{3}{2} x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\\therefore \frac{(3+\sqrt 3)}{2} x= 4(3+\sqrt 3)\\\\\therefore x = 4(3+\sqrt 3)\times \frac{2}{(3+\sqrt 3)}\\\\\therefore x = 4\cancel{(3+\sqrt 3)}\times \frac{2}{\cancel {(3+\sqrt 3)}}\\\\\therefore x = 4\times 2\\\\\therefore x = 8\\\\\huge\purple {\boxed{\implies MO = 8}} \: \\ [From\: equation \: (1)]\\\\\because MP = \frac{1}{2} x \: \\ [From\: equation \: (2)]\\\\\therefore MP = \frac{1}{2} \times 8\\\\\huge\red {\boxed{\therefore MP = 4 \: units}}](https://tex.z-dn.net/?f=%20In%5C%3A%20%5Ctriangle%20MOP%2C%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Cangle%20P%20%3D%2090%5Cdegree%20...%20%28given%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Cangle%20M%20%3D%2060%5Cdegree%20...%20%28given%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Cangle%20O%20%3D%2030%5Cdegree%283%5E%7Brd%7D%20%5C%3A%20%5Cangle%20%5C%3A%20of%5C%3A%20%5Ctriangle%29%20%5C%5C%3C%2Fp%3E%3Cp%3ELet%20%5Chuge%5Cpurple%20%7BMO%20%3D%20x%20%5C%3A%20units%7D...%20%281%29%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20MP%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20MO%5C%5C%28side%5C%3A%20opposite%20%5C%3A%20to%5C%3A%2030%5Cdegree%29%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20MP%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20x%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Chuge%5Cred%20%7B%5Ctherefore%20MP%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20x%7D....%20%282%29%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Ctherefore%20PO%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B2%7D%20%5Ctimes%20MO%5C%5C%28side%5C%3A%20opposite%20%5C%3A%20to%5C%3A%2060%5Cdegree%29%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20PO%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B2%7D%20%5Ctimes%20x%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Chuge%5Corange%7B%5Ctherefore%20PO%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B2%7Dx%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Cbecause%20MP%20%2B%20PO%20%2B%20MO%20%3D%20P%28%5Ctriangle%20MOP%29%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Cfrac%7B1%7D%7B2%7D%20x%2B%5Cfrac%7B%5Csqrt%203%7D%7B2%7Dx%2B%20x%20%3D%2012%2B4%5Csqrt%203%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Cfrac%7B1%7D%7B2%7D%20x%2Bx%2B%5Cfrac%7B%5Csqrt%203%7D%7B2%7Dx%3D%20%204%283%2B%5Csqrt%203%29%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Cfrac%7B3%7D%7B2%7D%20x%2B%5Cfrac%7B%5Csqrt%203%7D%7B2%7Dx%3D%20%204%283%2B%5Csqrt%203%29%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Cfrac%7B%283%2B%5Csqrt%203%29%7D%7B2%7D%20x%3D%20%204%283%2B%5Csqrt%203%29%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Ctherefore%20x%20%3D%204%283%2B%5Csqrt%203%29%5Ctimes%20%5Cfrac%7B2%7D%7B%283%2B%5Csqrt%203%29%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20x%20%3D%204%5Ccancel%7B%283%2B%5Csqrt%203%29%7D%5Ctimes%20%5Cfrac%7B2%7D%7B%5Ccancel%20%7B%283%2B%5Csqrt%203%29%7D%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Ctherefore%20x%20%3D%204%5Ctimes%202%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20x%20%3D%208%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Chuge%5Cpurple%20%7B%5Cboxed%7B%5Cimplies%20MO%20%3D%208%7D%7D%20%5C%3A%20%5C%5C%20%5BFrom%5C%3A%20equation%20%5C%3A%20%281%29%5D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5Cbecause%20MP%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20x%20%5C%3A%20%3C%2Fp%3E%3Cp%3E%5C%5C%20%5BFrom%5C%3A%20equation%20%5C%3A%20%282%29%5D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20MP%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%208%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Chuge%5Cred%20%7B%5Cboxed%7B%5Ctherefore%20MP%20%3D%204%20%5C%3A%20units%7D%7D%3C%2Fp%3E%3Cp%3E)