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Vesnalui [34]
3 years ago
14

What is the center of the circle described by the equation (x - 2)^2 +(y + 7)^2 =169

Mathematics
1 answer:
Marizza181 [45]3 years ago
4 0

Answer:

The center is (2, -7)

Step-by-step explanation:

A circle is given by

(x-h)^2 + (y-k)^2 = r^2

where(h,k) is the center and r is the radius

(x - 2)^2 +(y + 7)^2 =169

(x - 2)^2 +(y -  -7)^2 =13^2

The center is (2, -7) and the radius is 13

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Each of the following financial products will help you build credit history EXCEPT
Otrada [13]

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Step-by-step explanation:

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8 0
2 years ago
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
20n -5 - 3n + 10 pls help
artcher [175]

Answer:

17x+5

Step-by-step explanation:

Simplify the equation

8 0
3 years ago
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Phoenix [80]

Answer:

d x=+-3

Step-by-step explanation:

divide both sides by 2

4 0
3 years ago
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