Answer:
Step-by-step explanation:
( Being vertically opposite angles)
Vertically opposite angles are always equal.
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change it's sign
⇒
Collect like terms
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Subtract 18 from 50
⇒
Divide both sides of the equation by 2
⇒
Calculate
⇒
The value of x is 16
Now, let's find value of m<AFD :
( sum of angle in straight line )
plug the value of x
⇒
Multiply the numbers
⇒
Add the numbers
⇒
Move constant to R.H.S and change it's sign
⇒
Subtract 98 from 180
⇒
Value of m<AFD = 82
Hope I helped!
Best regards!!
Answer:
x>4
Step-by-step explanation:
Answer:
<h2>X =
</h2><h2>Y = 5y.</h2>
Step-by-step explanation:
We need to find the translation for which, (-3, 1) becomes (1, 5).
-3 will become 1, if it is divided by -3.
Hence, the translation for x axis is X = .
1 will become 5, when it is multiplied by 5.
Hence, The translation for y axis is Y = 5y.
Answer:
Only d) is false.
Step-by-step explanation:
Let 
be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that 
. 0 is a root of p, so we have that 
.
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.
