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rodikova [14]
2 years ago
14

In 5 batches of trail mix, there are 3 cups of chocolate chips. How many cups of chocolate chips are in 1 batch?​

Mathematics
1 answer:
Rina8888 [55]2 years ago
6 0

Answer:

5÷3=1.6666666667

so in 1 batch there would be 1.67 cups?

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Ron has to color in three shapes (square,circle and triangle) with different colors (red,blue,green). In how many different ways
Nataly [62]
Square-red,blue,green
circle-red,blue,green
triangle-red,blue,green

add them together which will equal 9
3 0
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
Start a conversation/argument in the comments
Digiron [165]

Answer:

What do we start a convo or an argumnet about...and why?

Step-by-step explanation:

but heres one : Donald Trump or Biden?

heheheheheheh

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What is 1/4 plus 1/3
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Answer:it would be 7/12 I think

Step-by-step explanation:

4 0
2 years ago
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On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an
ExtremeBDS [4]

Answer:

y\geq x-2

x+2y

Step-by-step explanation:

step 1

<em>Find the equation of the first inequality</em>

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{0+2}{2-0}

m=\frac{2}{2}

m=1

The equation in slope intercept form is equal to

y=mx+b

we have

m=1

b=-2 ---> the y-intercept is given

substitute

y=x-2

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

y\geq x-2

step 2

<em>Find the equation of the second inequality</em>

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{0-2}{4-0}

m=\frac{-2}{4}

m=-\frac{1}{2}

The equation in slope intercept form is equal to

y=mx+b

we have

m=-\frac{1}{2}

b=2 ---> the y-intercept is given

substitute

y=-\frac{1}{2}x+2

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

y

Rewrite

Multiply by 2 both sides

2y

x+2y

therefore

The system of inequalities is

y\geq x-2

x+2y

see the attached figure to better understand the problem

5 0
3 years ago
Read 2 more answers
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