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3 years ago

Write and equation of the line below

Mathematics

1 answer:

blondinia [14]3 years ago

4 0

Answer:

y = 1/4x + 0 or just y = 1/4x

Step-by-step explanation:

First I need the slope so I look at the dots and see how much boxes it goes up and then to the side. So it’s up 2 to the side 8. The slope would be 2/8 but you can simply it by 2 and you get 1/4. And the y intercept is given its zero.

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Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t

Svet_ta [14]

Answer:

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

$T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}$

$[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

$T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}$

$[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]$

Finally, the third vector of basis E is $e3(t)=t^{2}$

$T[e3(t)]=T(t^{2})$

in the equation : a2 = 1

$T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}$

Then

$[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]$

And that is the third column of [T]EE

Let's write our matrix

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

$X=\left[\begin{array}{c}1&0&0\\\end{array}\right]$

$AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

Applying the coordinates 2,6 and -2 to the basis E we obtain

$2+6t-2t^{2}$

That was the original result of T[e1(t)]

8 0

3 years ago

Which expression is equivalent to 3/24?

spin [16.1K]

Mmmmmmmmmmmmmoooooooooooooooooooooooooooooooooooooooooooooooooosssssssssssssssssssssssssssseeeeeeeeeeeeeeeeeeeeeeeee

5 0

3 years ago

How do you solve this problem? With work!!

Evgesh-ka [11]

You would put 9 times v because you are multiplying it to the 9 and you do not know what v is then you would divide it by 3 and get your answer so for example if you should have gotten 9 times v = 72 then 72 divided by 3 = 24 and 24 divided by 3 = 8

7 0

3 years ago

Read 2 more answers

Is (0, 0) a solution to the equation y = x?

Mandarinka [93]

Answer:

yes

Step-by-step explanation:

if both y and x are 0 than it is true that they equal each other since 0=0

8 0

4 years ago

Rose has 5 times as many stickers as John. They have 300 stickers in all. How many more stickers does Rose have than John? Show

kirill115 [55]

5x+x=300

6x=300

x=50

5(50)=250 (Rose)

x=50(John)

Rose has 250 stickers and John has 50, therefore Rose has 200 more stickers than John.

6 0

3 years ago

Read 2 more answers

Write and equation of the line below ​

Write and equation of the line below