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katovenus [111]
2 years ago
5

If the line segments and are drawn, which of the following conjectures is true?

Mathematics
1 answer:
padilas [110]2 years ago
4 0

Answer:

please provide context to your question.

Step-by-step explanation:

I can't help if theres not information to see.

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Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is reflection over the line y=1/2x
trapecia [35]

Answer:

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

Step-by-step explanation:

We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.

Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).

On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have

  • T(2,1) = (2,1)
  • T(-1,2) = (1,-2)

By summing the first vector with the double of the second one we get, using linearity

T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)

Hence, T(0,1) = (4/5,-3/5)

Now, we take the second vector and substract it the double of the first one (to kill the second variable)

T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)

Therefore, T(1,0) = (1,4/3)

The matrix A induced by  T has in its first column T(1,0) and in its second column T(0,1). We conclude that

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

3 0
3 years ago
Please answer this!!!!! im begging !!! pleaseeeeeeee
svlad2 [7]
This is really up to you. Also you Didn’t provide the assignment so this is impossible to answer, I can put anything in there. Just think about what you did and answer the questions yourself.
3 0
2 years ago
I also really need help with this question! <br> g(x)=2x - 3<br> h(x)=2x + 4<br> Find (g/h)(x)
Ray Of Light [21]
(2x-3)/(2(x+2))
x cannot equal -2
3 0
2 years ago
Hey this is another question ill give you brainliest and 5 stars as well as a heart<br><br> Asap pls
Dmitrij [34]

Answer:

e = s×0.72

Step-by-step explanation:

we need to find how much does a 1 song costs

so, 2.16 ÷ 3 = 0.72 $

4 0
2 years ago
Read 2 more answers
4x+1+8-x+5x-2=23 linear equations
DanielleElmas [232]

Step-by-step explanation:

= 4x-x+5x+1+8-2

=8x+7

proved##

5 0
2 years ago
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