10. What is the solution to the given equation? 8x - 3(2x

Find the value of y. 5 8 4 2 50 Pts!

Vinvika [58]

Answer and Explanation:

Since this is a 30-60-90 triangle, you can use the ratio of side lengths specific to this type of triangle:

x = 4√(2)

y = 2(4) = 8

because where 4 = T,

x = T√2 and y = 2T

so again:

$x = 4\sqrt{2}\\y = 8$

8 0

2 years ago

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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

Write .27 as a fraction in simplest form.

Debora [2.8K]

Answer:

27/100

Step-by-step explanation:

It's in the hundreths,

so we just put 27 over 100

8 0

2 years ago

Which number-line model represents the sum of 3/4 + ( - 1.75) ?

Fed [463]

Answer:

A

Step-by-step explanation:

6 0

3 years ago

Put 2/3 5/7 16/21 in order from least to greatest

hodyreva [135]

Answer:

5/7, 2/3, and 16/21

Step-by-step explanation:

If you put them all under the same denominator you will get 2/3=14/21, 5/7= 10/21, and 16/21. And if you put them in order it is 10/21, 14/21, and 16/21. Hope this helps, let me know if correct!!

5 0

3 years ago

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10. What is the solution to the given equation? 8x - 3(2x - 4) = 3(x-6)