X+3y=3
First add subtract the x
3y=-x+3
Then divide 3
Y=-1/3x+1
Answer:
The triangle ABC is an isosceles right triangle
Step-by-step explanation:
we have
The coordinates of triangle ABC are
A (0, 2), B (2, 5), and C (−1, 7)
we know that
An isosceles triangle has two equal sides and two equal internal angles
The formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
step 1
Find the distance AB
substitute in the formula
![d=\sqrt{(5-2)^{2}+(2-0)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285-2%29%5E%7B2%7D%2B%282-0%29%5E%7B2%7D%7D)
![d=\sqrt{(3)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![dAB=\sqrt{13}\ units](https://tex.z-dn.net/?f=dAB%3D%5Csqrt%7B13%7D%5C%20units)
step 2
Find the distance BC
substitute in the formula
![d=\sqrt{(7-5)^{2}+(-1-2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%287-5%29%5E%7B2%7D%2B%28-1-2%29%5E%7B2%7D%7D)
![d=\sqrt{(2)^{2}+(-3)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%282%29%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%7D)
![dBC=\sqrt{13}\ units](https://tex.z-dn.net/?f=dBC%3D%5Csqrt%7B13%7D%5C%20units)
step 3
Find the distance AC
substitute in the formula
![d=\sqrt{(7-2)^{2}+(-1-0)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%287-2%29%5E%7B2%7D%2B%28-1-0%29%5E%7B2%7D%7D)
![d=\sqrt{(5)^{2}+(-1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285%29%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D)
![dAC=\sqrt{26}\ units](https://tex.z-dn.net/?f=dAC%3D%5Csqrt%7B26%7D%5C%20units)
step 4
Compare the length sides
![dAB=\sqrt{13}\ units](https://tex.z-dn.net/?f=dAB%3D%5Csqrt%7B13%7D%5C%20units)
![dBC=\sqrt{13}\ units](https://tex.z-dn.net/?f=dBC%3D%5Csqrt%7B13%7D%5C%20units)
![dAC=\sqrt{26}\ units](https://tex.z-dn.net/?f=dAC%3D%5Csqrt%7B26%7D%5C%20units)
![dAB=dBC](https://tex.z-dn.net/?f=dAB%3DdBC)
therefore
Is an isosceles triangle
Applying the Pythagoras Theorem
![(AC)^{2} =(AB)^{2}+(BC)^{2}](https://tex.z-dn.net/?f=%28AC%29%5E%7B2%7D%20%3D%28AB%29%5E%7B2%7D%2B%28BC%29%5E%7B2%7D)
substitute
![(\sqrt{26})^{2} =(\sqrt{13})^{2}+(\sqrt{13})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B26%7D%29%5E%7B2%7D%20%3D%28%5Csqrt%7B13%7D%29%5E%7B2%7D%2B%28%5Csqrt%7B13%7D%29%5E%7B2%7D)
![26=13+13](https://tex.z-dn.net/?f=26%3D13%2B13)
-----> is true
therefore
Is an isosceles right triangle
An isosceles triangle is a triangle with 2 congruent sides. The congruent sides are called legs and the third side is called the base. So if 2 sides of a triangle have the same length, then we say that the triangle is isosceles.
M=12.2
(7^2)+(10^2)=149
the square root of 149 is 12.2
Step-by-step explanation:
Line segment = EG
point on a line segment = F
EG = 100
EF = 4x - 20
FG = 2x + 30
a/q, EF + FG = EG
the equation is
4x - 20 + 2x + 30 = 100
now solution for x is
→ 4x - 20 + 2x + 30 = 100
→ 6x + 10 = 100
→ 6x = 100 - 10 = 90
→ x = 90/6 = 15
therefore, value of x is 15.
and according to given information
EF = 4x - 20 = 4(15) - 20 = 60 - 20 = 40
FG = 2x + 30 = 2(15) + 30 = 30 + 30 = 60
hope this answer helps you dear..take care and may u have a great day ahead!