Answer: AE=13
Step-by-step explanation: took test
An isosceles triangle has two equal sides and one unique side
Hope this helps!
- Z
Answer:
here you go. hope this helps
Amount from dimes would be: 0.1y
Amount from quarters = 0.25x
So, total amount = 0.25x + 0.1y
So, she is not correct
Hope this helps!
Answer with Step-by-step explanation:
We are given that
and
are linearly independent.
By definition of linear independent there exits three scalar
and
such that
![a_1x_1+a_2x_2+a_3x_3=0](https://tex.z-dn.net/?f=a_1x_1%2Ba_2x_2%2Ba_3x_3%3D0)
Where ![a_1=a_2=a_3=0](https://tex.z-dn.net/?f=a_1%3Da_2%3Da_3%3D0)
![y_1=x_2+x_1,y_2=x_3+x_2,y_3=x_3+x_1](https://tex.z-dn.net/?f=y_1%3Dx_2%2Bx_1%2Cy_2%3Dx_3%2Bx_2%2Cy_3%3Dx_3%2Bx_1)
We have to prove that
and
are linearly independent.
Let
and
such that
![b_1y_1+b_2y_2+b_3y_3=0](https://tex.z-dn.net/?f=b_1y_1%2Bb_2y_2%2Bb_3y_3%3D0)
![b_1(x_2+x_1)+b_2(x_3+x_2)+b_3(x_3+x_1)=0](https://tex.z-dn.net/?f=b_1%28x_2%2Bx_1%29%2Bb_2%28x_3%2Bx_2%29%2Bb_3%28x_3%2Bx_1%29%3D0)
![b_1x_2+b_1x_1+b_2x_3+b_2x_2+b_3x_3+b_3x_1=0](https://tex.z-dn.net/?f=b_1x_2%2Bb_1x_1%2Bb_2x_3%2Bb_2x_2%2Bb_3x_3%2Bb_3x_1%3D0)
![(b_1+b_3)x_1+(b_2+b_1)x_2+(b_2+b_3)x_3=0](https://tex.z-dn.net/?f=%28b_1%2Bb_3%29x_1%2B%28b_2%2Bb_1%29x_2%2B%28b_2%2Bb_3%29x_3%3D0)
![b_1+b_3=0](https://tex.z-dn.net/?f=b_1%2Bb_3%3D0)
...(1)
![b_1+b_2=0](https://tex.z-dn.net/?f=b_1%2Bb_2%3D0)
..(2)
![b_2+b_3=0](https://tex.z-dn.net/?f=b_2%2Bb_3%3D0)
..(3)
Because
and
are linearly independent.
From equation (1) and (3)
...(4)
Adding equation (2) and (4)
![2b_1==0](https://tex.z-dn.net/?f=2b_1%3D%3D0)
![b_1=0](https://tex.z-dn.net/?f=b_1%3D0)
From equation (1) and (2)
![b_3=0,b_2=0,b_3=0](https://tex.z-dn.net/?f=b_3%3D0%2Cb_2%3D0%2Cb_3%3D0)
Hence,
and
area linearly independent.