Answer:
2.8, 4.5, 5.3
numbers represent the measure of the sides of a right triangle.
2.8²+4.5²=5.3²
7.84+20.25=28.09
28.09=28.09
Answer:
No
Step-by-step explanation:
If you fill in
4=-5(2)
4=-10
which is not true so therefore it is wrong.
Answer:
An irrational number is infinte and has no clear pattern. 3.33333 or .686868686868 would not be considered irrational because there is a clear pattern, but 5.432523421672389... would not be considered rational because the numbers it consists of are all random.
Answer:
The answer is below
Step-by-step explanation:
The equation of the line passing through two points is given by:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C)
The equation of line AB is:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{4-(-1)}{6-7}(x-7)\\\\y+1=-5(x-7)\\y+1=-5x+35\\y=-5x+34](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C%5C%5Cy-%28-1%29%3D%5Cfrac%7B4-%28-1%29%7D%7B6-7%7D%28x-7%29%5C%5C%5C%5Cy%2B1%3D-5%28x-7%29%5C%5Cy%2B1%3D-5x%2B35%5C%5Cy%3D-5x%2B34)
The midpoint of two lines is given as:
![x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+6}{2}=6.5, y=\frac{-1+4}{2}=1.5\\ = (6.5,1.5)](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%20y%3D%5Cfrac%7By_1%2By_2%7D%7B2%7D%5C%5Cmidpoint%5C%20of%5C%20AB%20%5C%20is%3A%5C%5Cx%3D%5Cfrac%7B7%2B6%7D%7B2%7D%3D6.5%2C%20y%3D%5Cfrac%7B-1%2B4%7D%7B2%7D%3D1.5%5C%5C%20%3D%20%286.5%2C1.5%29)
The equation of line AC is:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-1)=\frac{5-(-1)}{5-7}(x-7)\\\\y+1=-3(x-7)\\y+1=-3x+21\\y=-3x+20](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C%5C%5Cy-%28-1%29%3D%5Cfrac%7B5-%28-1%29%7D%7B5-7%7D%28x-7%29%5C%5C%5C%5Cy%2B1%3D-3%28x-7%29%5C%5Cy%2B1%3D-3x%2B21%5C%5Cy%3D-3x%2B20)
The midpoint of two lines is given as:
![x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}\\midpoint\ of\ AB \ is:\\x=\frac{7+5}{2}=6, y=\frac{-1+5}{2}=2\\ = (6,2)](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%20y%3D%5Cfrac%7By_1%2By_2%7D%7B2%7D%5C%5Cmidpoint%5C%20of%5C%20AB%20%5C%20is%3A%5C%5Cx%3D%5Cfrac%7B7%2B5%7D%7B2%7D%3D6%2C%20y%3D%5Cfrac%7B-1%2B5%7D%7B2%7D%3D2%5C%5C%20%3D%20%286%2C2%29)
The product of the slope of a perpendicular bisector of a line and the slope of the line is -1. That is m1m2 = -1
The slope of the perpendicular bisector of AB is:
m(-5)=-1
m=1/5
The equation of the perpendicular bisector of AB passing through (6.5,1.5) is:
![y-y_1=m(x-x_1)\\y-1.5=\frac{1}{5}(x-6.5)\\y=\frac{1}{5} x-8.25](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5Cy-1.5%3D%5Cfrac%7B1%7D%7B5%7D%28x-6.5%29%5C%5Cy%3D%5Cfrac%7B1%7D%7B5%7D%20x-8.25)
The slope of the perpendicular bisector of AB is:
m(-3)=-1
m=1/3
The equation of the perpendicular bisector of AB passing through (6,2) is:
![y-y_1=m(x-x_1)\\y-2=\frac{1}{3}(x-7)\\y=\frac{1}{3} x-4.33](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5Cy-2%3D%5Cfrac%7B1%7D%7B3%7D%28x-7%29%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7D%20x-4.33)
2) The point of intersection is gotten by solving y = 1/5 x -8.25 and y = 1/3 x-4.33 simultaneously.
Subtracting the two equations from each other gives:
0= -0.133x - 3.92
-0.133x = 3.92
x = -29.5
Put x = -29.5 in y = 1/5 x -8.25 i.e:
y = 1/5 (29.5) -8.25
y = -14.16
The point of intersection is (-29.5, -14.16)
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