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2 years ago

Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (5, 2), (3, 3)

Mathematics

2 answers:

Strike441 [17]2 years ago

8 0

Answer:

-0.5

Step-by-step explanation:

slope=rise/run or y/x in other words(y2-y1/x2-x1)
(y2-y1) is 3-2 so y2-y1=1
(x2-x1) is 3-5 so x2-x1= -2
-1/2 or -0.5 would be the slope.

Sindrei [870]2 years ago

8 0

Answer:

1/-2

Step-by-step explanation:

5 = x1, 2 = y1

3 = x2, 3 = y2

y is always before x

y2 - y1 = 3 - 2

3 - 2 = 1

You can always subtract y1 by y2, but I am just doing it the other way. But if you choose to subtract 2 by 1, you have t do that for x also.

x2 - x1 = 3 - 5

3 - 5 = -2

After this step, you put y on top, and x on the bottom, making:

1/-2

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Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are

alexgriva [62]

Answer:

$P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)$

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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If the absolute value of a number is added to the original number will the sum always equal 0

lbvjy [14]

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Troyanec [42]

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16) 1420 2x A) 67 C) 68 B) 71 D) 73 What is the value of x???

larisa [96]

Answer:

x = 710

Step-by-step explanation:

1. Divide both sides by 2 to get x by itself

1420 = 2x

↓

1420 ÷ 2 = 2x ÷ 2

↓

710 = x

2. Switch sides

710 = x

↓

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larisa [96]

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