Answer:To subtract 7 from 102, you have to regroup. You subtract 2 from 100, and 2 from 7, so it is 100-5. 100-5 is 95. The answer is 95. If you don't understand, tell me in the comments. This is just one method of subtracting.
Step-by-step explanation:
Let
be the measure of the angle labeled in the attached image below. By the law of sines,
![\dfrac{\sin\theta}{10x+5}=\dfrac{\sin(\pi-\varphi)}{78}=\dfrac{\sin\varphi}{78}\implies\sin\varphi=\dfrac{78\sin\theta}{10x+5}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%5Ctheta%7D%7B10x%2B5%7D%3D%5Cdfrac%7B%5Csin%28%5Cpi-%5Cvarphi%29%7D%7B78%7D%3D%5Cdfrac%7B%5Csin%5Cvarphi%7D%7B78%7D%5Cimplies%5Csin%5Cvarphi%3D%5Cdfrac%7B78%5Csin%5Ctheta%7D%7B10x%2B5%7D)
and
![\dfrac{\sin\theta}{6x-1}=\dfrac{\sin\varphi}{42}\implies\sin\varphi=\dfrac{42\sin\theta}{6x-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%5Ctheta%7D%7B6x-1%7D%3D%5Cdfrac%7B%5Csin%5Cvarphi%7D%7B42%7D%5Cimplies%5Csin%5Cvarphi%3D%5Cdfrac%7B42%5Csin%5Ctheta%7D%7B6x-1%7D)
Then
![\dfrac{78\sin\theta}{10x+5}=\dfrac{42\sin\theta}{6x-1}\implies78(6x-1)=42(10x+5)](https://tex.z-dn.net/?f=%5Cdfrac%7B78%5Csin%5Ctheta%7D%7B10x%2B5%7D%3D%5Cdfrac%7B42%5Csin%5Ctheta%7D%7B6x-1%7D%5Cimplies78%286x-1%29%3D42%2810x%2B5%29)
From here we can solve for
:
.
Answer:
look at the pivots (the leading 1's of the rows)
Step-by-step explanation:
Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.
I think it’s D I can’t read the question that well but it should be C or D