Help!!! I don’t know what to do

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

#SPJ10

5 0

2 years ago

I Need HelpAsap please I will mark you brainlist

Arada [10]

Answer:

a. 72 inches

b. 21.3 inches

Step-by-step explanation:

12:27

a. 32 inches in height

32/x = 12/27

Set these fractions equal to each other

32= 12

12 times 2.6(repeating decimal) equals 32

So to find the width do 2.666... time 27 and you get 72 inches.

---------------------------------------------------------------------------

b. 48 inches in width

Again set the fractions equal to each other.

x/48 = 12/27

48 divided by 27 equals 1.77777....

To get height, do 1.77777.... times 12 and you get 21.3333333

But since it is to the nearest tenth, you get 21.3 inches

Hope that helps!

5 0

3 years ago

An empty bucket weighs 800g.

erica [24]

Answer:

412.5 percent

7 0

3 years ago

Read 2 more answers

Hester sells televisions. She earns a fixed amount for each television and an additional $ 15 if the buyer gets an extended war

tiny-mole [99]

Answer:

$y =mx +bx$

Where y is the total amount earned, m the amount for each extended warranty and b the fixed cost and x the total amount of TVs

For this case the value of x = 16 since we have 16 Tvs with extended warranties and we can do this:

$1200 = 15*16 +16b$

and solving for b we got:

$b= \frac{1200-15*16}{16}= 60$

And then we can conclude that she earns 60 for each TV

Step-by-step explanation:

For this case we can set a linear model like this:

$y =mx +bx$

Where y is the total amount earned, m the amount for each extended warranty and b the fixed cost and x the total amount of TVs

For this case the value of x = 16 since we have 16 Tvs with extended warranties and we can do this:

$1200 = 15*16 +16b$

and solving for b we got:

$b= \frac{1200-15*16}{16}= 60$

And then we can conclude that she earns 60 for each TV

8 0

3 years ago

What is 120/180 in simplest form

dlinn [17]

You can find the simplest form of 120/180 by rounding down the numbers. you can take the zeros away and your left with 12/18. you can make it even smaller by using the 6 time tables. 12 and 18 are both in the 6 time tables. 2×6=12 and 3×6=18. The answer is 2/3.

Hope I helped :D

6 0

3 years ago