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pogonyaev
3 years ago
12

An item is regularly priced at $85. it is on sale for 60% off the regular price. How much ( in dollars) is discounted from the r

egular price?
Mathematics
1 answer:
MaRussiya [10]3 years ago
5 0

hvhAnswer:

gfhh

Step-by-step explanation:

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-5x^5+35x^4-30x^3 can someone help me pls
vampirchik [111]

Answer:

if im correct -5^3

Step-by-step explanation:

7 0
3 years ago
Q1.The cost of $16.50 for the music was reduction of 12% on the original cost.
NNADVOKAT [17]
Q1) £16.50 x 1.12 = £18.48
Q2)

2+9+1= 12
3h 33m = 213m
213/12 = 17.75
2x17.75 = 35.5 (music)
9x17.75 = 159.75 (films)
1x17.75 = 17.75 (books)

So it’s 159.75 minutes for the films to download
7 0
3 years ago
Solve for x: 3x+6>-15 x=?
kati45 [8]

Answer:

x>-7

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Asap, round to nearest tenth
Amiraneli [1.4K]

Answer:

A

Step-by-step explanation:

6 0
2 years ago
(1) (10 points) Find the characteristic polynomial of A (2) (5 points) Find all eigenvalues of A. You are allowed to use your ca
Yuri [45]

Answer:

Step-by-step explanation:

Since this question is lacking the matrix A, we will solve the question with the matrix

\left[\begin{matrix}4 & -2 \\ 1 & 1 \end{matrix}\right]

so we can illustrate how to solve the problem step by step.

a) The characteristic polynomial is defined by the equation det(A-\lambdaI)=0 where I is the identity matrix of appropiate size and lambda is a variable to be solved. In our case,

\left|\left[\begin{matrix}4-\lamda & -2 \\ 1 & 1-\lambda \end{matrix}\right]\right|= 0 = (4-\lambda)(1-\lambda)+2 = \lambda^2-5\lambda+4+2 = \lambda^2-5\lambda+6

So the characteristic polynomial is \lambda^2-5\lambda+6=0.

b) The eigenvalues of the matrix are the roots of the characteristic polynomial. Note that

\lambda^2-5\lambda+6=(\lambda-3)(\lambda-2) =0

So \lambda=3, \lambda=2

c) To find the bases of each eigenspace, we replace the value of lambda and solve the homogeneus system(equalized to zero) of the resultant matrix. We will illustrate the process with one eigen value and the other one is left as an exercise.

If \lambda=3 we get the following matrix

\left[\begin{matrix}1 & -2 \\ 1 & -2 \end{matrix}\right].

Since both rows are equal, we have the equation

x-2y=0. Thus x=2y. In this case, we get to choose y freely, so let's take y=1. Then x=2. So, the eigenvector that is a base for the eigenspace associated to the eigenvalue 3 is the vector (2,1)

For the case \lambda=2, using the same process, we get the vector (1,1).

d) By definition, to diagonalize a matrix A is to find a diagonal matrix D and a matrix P such that A=PDP^{-1}. We can construct matrix D and P by choosing the eigenvalues as the diagonal of matrix D. So, if we pick the eigen value 3 in the first column of D, we must put the correspondent eigenvector (2,1) in the first column of P. In this case, the matrices that we get are

P=\left[\begin{matrix}2&1 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}3&0 \\ 0 & 2 \end{matrix}\right]

This matrices are not unique, since they depend on the order in which we arrange the eigenvalues in the matrix D. Another pair or matrices that diagonalize A is

P=\left[\begin{matrix}1&2 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}2&0 \\ 0 & 3 \end{matrix}\right]

which is obtained by interchanging the eigenvalues on the diagonal and their respective eigenvectors

4 0
3 years ago
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