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3 years ago

5

Which pair of lines are perpendicular to one another ?

1 answer:

Ronch [10]3 years ago

8 0

Lines are perpendicular to each other when their slopes are of the opposite parity (plus or minus) and the reciprocal of each other. I will check the answer that you have given. Already, in one of the equations, (y - 3 = 4/7x)we can see the slope. Now we just need to find the slope in 7x+4y=20. We can do this by isolating y and then getting y by itself. Doing this, we get:

4y = -7x + 20
y = -7/4x + 5

Since we can see that the slopes of the two lines multiply to negative one, then you are right, the two lines are parallel.

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Assume that T is a linear transformation. Find the standard matrix of T. T: R^3 right arrow R^2 , T(e 1) =(1,2), and T(e2 ) =( -

irina [24]

Answer:

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

Step-by-step explanation:

Given

$T:R^3->R^2$

$T(e_1) = (1,2)$

$T(e_2) = (-4,6)$

$T(e_3) = (2,-6)$

Required

Find the standard matrix

The standard matrix (A) is given by

$Ax = T(x)$

Where

$T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]$

$Ax = T(x)$ becomes

$Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]$

The x on both sides cancel out; and, we're left with:

$A = [T(e_1)\ T(e_2)\ T(e_3)]$

Recall that:

$T(e_1) = (1,2)$

$T(e_2) = (-4,6)$

$T(e_3) = (2,-6)$

In matrix:

$(a,b)$ is represented as: $\left[\begin{array}{c}a\\b\end{array}\right]$

So:

$T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]$

$T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]$

$T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]$

Substitute the above expressions in $A = [T(e_1)\ T(e_2)\ T(e_3)]$

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

Hence, the standard of the matrix A is:

$A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]$

6 0

3 years ago

Help pleaseeeeeeeeeeeeee

Dennis_Churaev [7]

Answer:

D^1 should be (28,0)

Step-by-step explanation:

a dilation is performed by multiplying the x and y coordinates by the scale factor. D(7,0)... (7×4,0×4).... D^1(28,0)

4 0

3 years ago

A bag contains 50 tokens: 20 pink ,13 blue and 17 purble.if a person selects one token, replaces it,and then selects a second to

stiv31 [10]

Answer:

Step-by-step explanation:

this is independent

20/50= 2/5= 40% of getting pink, probability of getting 2= 20%

13/50=0.26= 26% of getting blue, probability of getting 2= 13%

17/50=0.34=34% of getting purple, probability of getting 2 = 17%

70%

5 0

2 years ago

What is the pattern 3.5 to 13

mars1129 [50]

Adding 9.5 every time

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3 years ago

Jessica drank 1/8 gallon of orange juice

irakobra [83]

And what else you can not solve that problem

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3 years ago