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3 years ago

Using the discriminatory, determine the number of real solution 2x^2+7x-15=0

Mathematics

1 answer:

Scilla [17]3 years ago

6 0

Answer:

c. two real solutions

Step-by-step explanation:

x = -5 , x = 1.5

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. Complete. y2 + 15y + 56 = (y + 7)(y +)

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In this equation when it says y2 do you mean 2y or no

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3 years ago

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Write the slope-intercept form of the equation of each line given the slope and y-

rewona [7]

Answer:

1x - y + 3 = 0

Step-by-step explanation:

y = 1(x) + 3

y = 1x + 3

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3 years ago

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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3 years ago

Suppose 12 quarts of pure antifreeze is mixed with 8 quarts of a solution that is 72% antifreeze. Answer the questions below. Do

ra1l [238]

(a)

12+0.72(8)

12+5.76

17.76 qts of antifreeze

(b)

100(12+8(.72))/(12+8)

100(12+5.76)/20

100(17.76)/20

5(17.76)

88.8%

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3 years ago

If a $200 billion increase in investment spending creates $200 billion of new income in the first round of the multiplier proces

telo118 [61]

The multiplier would be 4, I believe so.

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3 years ago