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Nat2105 [25]
3 years ago
14

What is 1036.50 rounded the the nearest whole number?

Mathematics
1 answer:
Pavel [41]3 years ago
4 0
1037 is the whole number estimate
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The pentagon shown could be reflected over which line to be carried onto itself?
Svetach [21]

Answer:

paraell

Step-by-step explanation:

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3 years ago
A painter is using a 8-foot ladder to paint a house. The painter places the ladder 4 feet from the house. How high up the wall d
zavuch27 [327]

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32 feet high

Step-by-step explanation:

7 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
Write a polynomial that represents the area of the shaded region
marusya05 [52]
<h3>Answer: x^2-3x+36</h3>

=========================================

Explanation:

The larger rectangle has area of (x+1)(x+1) = x^2+2x+1 through the use of the FOIL rule or distribution

If you use distribution, then it might help to let y = x+1 so we'd have y(x+1) lead to xy+1y which becomes x(x+1)+1(x+1). From there it might be easier to see how to get x^2+2x+1 after everything distributes again and simplifies.

The smaller rectangle has area 5x-35 which is found by distributing 5(x-7)

To get the shaded area, we subtract the two rectangle areas found above

shaded area = (larger area) - (smaller area)

shaded area = (x^2+2x+1) - (5x - 35)

shaded area = x^2+2x+1 - 5x + 35

shaded area = x^2-3x+36

6 0
3 years ago
Please help me with these 2 questions!!
IceJOKER [234]

Answer: 53. B similar

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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