Find the area of a triangle when a = 5, B = 37º, and C= 84º

If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

alexgriva [62]

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$

So, no option is correct. And the answer is

$T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$

Learn more about linear transformations here-

brainly.com/question/13005179

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5 0

2 years ago

Can please help!

sukhopar [10]

Answer:
equation is: width = area / length
width = 62.5 yd

Explanation:
For the first rectangle:
We have:
length = 75 yd and width = 60 yd
Therefore:
area = length * width
area = 75 * 60
area = 4500 yd²

For the second rectangle:
We have:
area = area of first rectangle = 4500 yd²
length = 72 yd
area = length * width
width = area / length ............> The required equation
width = 4500 / 72
width = 62.5 yd

Hope this helps :)

5 0

3 years ago

Write a real world problem that involves classifying a quadrilateral then solve the problem.

Anastasy [175]

An amusement park ride has a moving platform attached to four swinging arms. The platform swings back and forth, higher and higher, until it goes over the top and around in a circular motion. In the diagram below, AD and BC represent two of the swinging arms, and DC <span>is parallel to the ground
</span>(line l). Explain why the moving platform AB <span>is always parallel to the ground.</span>

5 0

3 years ago

Can the square of an integer be a negative number? Explain.

ivolga24 [154]

Answer: how ever no negative number can really have a square root however it is possile to wokr with a more incluesive set of number so i belive no

Step-by-step explanation:

5 0

3 years ago

Look at the picture and match

Yuliya22 [10]

Answer: 1. 2rs is 2 . r . s = 2rs 2. 18rst is 2 . 3 . 3 r. s. t = 18rst

3. 25ab is 5 . 5 a . b = 25ab 4. 30abc is 2 . 3 . 5 a . b . c= 30abc 5. 45abr is 3 . 3 . 5 . a . b . r

Step-by-step explanation: 2. 18rst is 2 . 3 . 3 . r . s . t because 2 x 3 = 6 x 3 = 18rst.

3. 25ab is 5 . 5 a . b because 5 x 5 = 25ab

4. 30abc is 2 . 3 . 5 a . b because 2 x 3 = 6 x 5 = 30abc.

5. 45abr is 3 . 3 . 5 . a . b . r because 3 x 3 = 9 x 5 = 45abr.

Hope this works! :) If not, I am sorry :(. If it does, Your Welcome! :)

3 0

3 years ago

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