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kipiarov [429]
2 years ago
14

What is the value of x? The figure is not drawn to scale. Show work

Mathematics
1 answer:
Alecsey [184]2 years ago
8 0

Answer:

x = 21.

Step-by-step explanation:

AS there are parallel lines:

4/12 = 7/x

4x = 84

x = 84/4 = 21.

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An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false
asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1) 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 p(\lambda)=\det(B-\lambda I). 0 is a root of p, so we have that p(0)=\det(B-0 I)=\det B=0.

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.      

8 0
3 years ago
I am a number. I am the
LenaWriter [7]

Answer:

3

Step-by-step explanation:

to find side length of squares take square root of areas

first square side length: 9

second square side length: 6

difference between 9 and 6 is subtraction, 9-6=3

4 0
3 years ago
Besides 12 and 1, what is one factor of 12
BabaBlast [244]
One factor of 12 is 2. The other factors of 12 are 3, 4, and 6.
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cestrela7 [59]

Answer:

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Step-by-step explanation:

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I need help please!!!
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B

Step-by-step explanation:

7 0
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