Answer:
(a) Side lengths
![RT = \sqrt{18}](https://tex.z-dn.net/?f=RT%20%3D%20%5Csqrt%7B18%7D)
(b) Slope
![ST = -4](https://tex.z-dn.net/?f=ST%20%3D%20-4)
(c) Scalene triangle
Step-by-step explanation:
Given
![R = (2,3)](https://tex.z-dn.net/?f=R%20%3D%20%282%2C3%29)
![S = (4,4)](https://tex.z-dn.net/?f=S%20%3D%20%284%2C4%29)
![T = (5,0)\\](https://tex.z-dn.net/?f=T%20%3D%20%285%2C0%29%5C%5C)
Solving (a): Length of each side
This is calculated using distance formula
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
So, we have:
![RS = \sqrt{(4 - 2)^2 + (4 - 3)^2}](https://tex.z-dn.net/?f=RS%20%3D%20%5Csqrt%7B%284%20-%202%29%5E2%20%2B%20%284%20-%203%29%5E2%7D)
![RS = \sqrt{5}](https://tex.z-dn.net/?f=RS%20%3D%20%5Csqrt%7B5%7D)
![ST = \sqrt{(5 - 4)^2 + (0- 4)^2}](https://tex.z-dn.net/?f=ST%20%3D%20%5Csqrt%7B%285%20-%204%29%5E2%20%2B%20%280-%204%29%5E2%7D)
![ST = \sqrt{17}](https://tex.z-dn.net/?f=ST%20%3D%20%5Csqrt%7B17%7D)
![RT = \sqrt{(5 - 2)^2 + (0 - 3)^2}](https://tex.z-dn.net/?f=RT%20%3D%20%5Csqrt%7B%285%20-%202%29%5E2%20%2B%20%280%20-%203%29%5E2%7D)
![RT = \sqrt{18}](https://tex.z-dn.net/?f=RT%20%3D%20%5Csqrt%7B18%7D)
Solving (b): The slope of each side
This is calculated using:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
So, we have:
![RS = \frac{4- 3}{4- 2}](https://tex.z-dn.net/?f=RS%20%3D%20%5Cfrac%7B4-%203%7D%7B4-%202%7D)
![RS = \frac{1}{2}](https://tex.z-dn.net/?f=RS%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
![RT = \frac{0 - 3}{5- 2}](https://tex.z-dn.net/?f=RT%20%3D%20%5Cfrac%7B0%20-%203%7D%7B5-%202%7D)
![RT = \frac{ - 3}{- 3}](https://tex.z-dn.net/?f=RT%20%3D%20%5Cfrac%7B%20-%203%7D%7B-%203%7D)
![RT = 1](https://tex.z-dn.net/?f=RT%20%3D%201)
![ST = \frac{0 - 4}{5- 4}](https://tex.z-dn.net/?f=ST%20%3D%20%5Cfrac%7B0%20-%204%7D%7B5-%204%7D)
![ST = \frac{- 4}{1}](https://tex.z-dn.net/?f=ST%20%3D%20%5Cfrac%7B-%204%7D%7B1%7D)
![ST = -4](https://tex.z-dn.net/?f=ST%20%3D%20-4)
Solving (c): Classify the triangle
In (a), we have:
![RS = \sqrt{5}](https://tex.z-dn.net/?f=RS%20%3D%20%5Csqrt%7B5%7D)
![ST = \sqrt{17}](https://tex.z-dn.net/?f=ST%20%3D%20%5Csqrt%7B17%7D)
![RT = \sqrt{18}](https://tex.z-dn.net/?f=RT%20%3D%20%5Csqrt%7B18%7D)
None of the sides are equal;
The triangle is scalene
Answer:
50% chance
Step-by-step explanation:
4 * 50% = 2
Answer: the original cost of the item is 90$
Step-by-step explanation:
30% off of the item = 27$
27 dollar is 30% of the item
thus 27 = 0.30X
0.30X = 27
time both side by 10
3X = 270
270/3 = 90