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Advocard [28]
3 years ago
13

Evaluate 10.2x + 9.4y when x = 2 and y = 3.

Mathematics
1 answer:
IrinaK [193]3 years ago
7 0

Answer:

48.6

Step-by-step explanation:

Substitute 2 for x and 3 for y

Multiply

Simplify by rounding then add to arrive at

Answer

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Round 1.6 to the nearest whole number
Elden [556K]

Answer:

The Answer is 2

Step-by-step explanation:

The rule is 4 or less let it rest. 5 or more raise the score.  6 is greater than 5 so you raise it to two

3 0
2 years ago
Read 2 more answers
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

3 0
3 years ago
Please help me tysm :)
aivan3 [116]

Answer:

asdasd

Step-by-step explanation:

3 0
3 years ago
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The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further from the lighthouse. The new bearing is 25°
djverab [1.8K]

Answer:

The distance between the ship at N 25°E and the lighthouse would be 7.26 miles.

Step-by-step explanation:

The question is incomplete. The complete question should be

The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further towards the south. The new bearing is N 25°E. What is the distance between the lighthouse and the ship at the new location?

Given the initial bearing of a lighthouse from the ship is N 37° E. So, \angle ABN is 37°. We can see from the diagram that \angle ABC would be 180-37= 143°.

Also, the new bearing is N 25°E. So, \angle BCA would be 25°.

Now we can find \angle BAC. As the sum of the internal angle of a triangle is 180°.

\angle ABC+\angle BCA+\angle BAC=180\\143+25+\angle BAC=180\\\angle BAC=180-143-25\\\angle BAC=12

Also, it was given that ship sails 2.5 miles from N 37° E to N 25°E. We can see from the diagram that this distance would be our BC.

And let us assume the distance between the lighthouse and the ship at N 25°E is AC=x

We can apply the sine rule now.

\frac{x}{sin(143)}=\frac{2.5}{sin(12)}\\ \\x=\frac{2.5}{sin(12)}\times sin(143)\\\\x=\frac{2.5}{0.207}\times 0.601\\ \\x=7.26\ miles

So, the distance between the ship at N 25°E and the lighthouse is 7.26 miles.

3 0
3 years ago
The pyramid shown has a square base that is 12 centimeters on each side. The slant height is 18 centimeters. What is the surface
iogann1982 [59]
A = 576 cm2 hope that helps ;)<span>
</span>
8 0
3 years ago
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