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Nady [450]
2 years ago
12

A sofa is on sale for 73% off. The sale price is $172.80. What is the regular price?

Mathematics
2 answers:
Lapatulllka [165]2 years ago
7 0
To get the answer you have to divide the sale price $172.80 by 73%.
So first you turn 73% into a decimal by moving the decimal two places to the left turning it into .73 

$172.80 divided by .73 = $236.71

You can check by then multiplying $236.71 with .73 
myrzilka [38]2 years ago
7 0
The sale price is 27% so we multiply 172.80 by 3 to get a total of  518.40 which is 81% of the original cost but now how do we find the other 19%? well 172.80 divided by .27 gives us 6.40 all we have to do is do the equation 6.40*19 which is  121.60 now we add 518.40 with 121.60 to get 640.00
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Answer:

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Step-by-step explanation:

It is a result that a matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.  According with the data you provided the matrix should be

A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)

We know that its eigenvalues are \lambda_{1}=-14, \lambda_{2}=-5, where \lambda_{2}=-5 has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle,E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle..

With this in mind we can form the matrices P, D that diagonalizes the matrix A so.

P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)

and

D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)

Observe that the rows of P are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of P dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

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Answer:

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Step-by-step explanation:

Set up a proportion to solve this...

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Step-by-step explanation:

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