8 times 5 minus 2 plus 4 divided by 2 equals 33 when

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-

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5 0

2 years ago

What is the square root of 50?

notka56 [123]

Answer:

√50= 5√2

Step-by-step explanation:

50=25*2

√50=√25*2

√50=√5*5*2

√50= 5√2

3 0

3 years ago

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The formula s=12at ^2 is used to calculate the distance s travelled by a bike when a=3 and t=10, each correct to the nearest int

seraphim [82]

Answer:

Step-by-step explanation:

Given the formula for calculating the distance travelled expressed as;

s=1/2at^2

Given

a = 3

t = 10

Required

lower bound of s

Substitute the given values into the equation;

s=1/2at^2

S = 1/2(3)(10)^2

S = 1/2 * 3 * 100

S = 3 * 50

S = 150

Hence the lower bound of distance S is 150

8 0

3 years ago

3x - y = 0 2x - y = 1

9966 [12]

Answer: See below

Explanation:
Solve this system of equation using elimination method:

3x - y = 0
2x - y = 1
________
3x - y = 0
-1(2x - y = 1)
_________
3x - y = 0
-2x + y = -1
_________
X = -1

We know that x = -1 now let’s plug it in the one of the equation to find y:

2x - y = 1
2(-1) - y = 1
-2 - y = 1
-y = 3
y = -3

8 0

3 years ago

What are the steps to converting 720 seconds into hours?

Nataly [62]

This conversion of 720 seconds to hours has been calculated by multiplying 720 seconds by 0.0002 and the result is 0.2 hours.

3 0

3 years ago

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