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Alisiya [41]
3 years ago
10

PLEASE HELP ME...

Mathematics
2 answers:
adell [148]3 years ago
4 0

Since the reflected figure is moved to the third quardrant, the reflection should be across the x-axis.

Also, if we compare the width and height of the orginial triangle with that of the reflected one, it is clear that it is dilated with a scale factor of 0.25.


erastovalidia [21]3 years ago
4 0

Answer:

Triangle ABC can be mapped onto triangle DEF with a reflection across the x axis followed by a dilation centered at the origin with a scale factor of 0.25 .

Step-by-step explanation:

Given : Graph of two triangle ABC and DEF with coordinates .

To find : Triangle ABC can be mapped onto triangle DEF with a reflection across the______ followed by a dilation centered at the origin with a scale factor of ______.

Solution : We can see from given graph triangle triangle ABC is reflected across  x axis.

Scale factor: 0.25

Therefore, Triangle ABC can be mapped onto triangle DEF with a reflection across the x axis followed by a dilation centered at the origin with a scale factor of 0.25 .

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Find the values of λ for which the determinant is zero.
elena55 [62]

Answer:

Determinant are special number that can only be defined for square matrices.

Step-by-step explanation:

Determinant are particularly important for analysis. The inverse of a matrix exist, if the determinant is not equal to zero.

How to find determinant

For a 2×2 matrix

det ( \left[\begin{array}{cc}x&y\\a&z\end{array}\right] ) = xz-ay

For a 3×3 matrix

we first decompose it to 2×2

det (\left[\begin{array}{ccc}k&l&m\\o&p&q\\r&s&t\end{array}\right] )\\\\= k*det(\left[\begin{array}{cc}p&q\\s&t\end{array}\right] ) - l*det(\left[\begin{array}{cc}o&q\\r&t\end{array}\right] ) + m*det(\left[\begin{array}{cc}o&p\\r&s\end{array}\right] ) \\\\=k(pt-sq) - l(ot-rq) + m(os-rp)

Example

Find the values of λ for which the determinant is zero

\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right]

det(\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right])\\\\= s*det(\left[\begin{array}{cc}s&-1\\-1&1\end{array}\right] ) - (-1)*det(\left[\begin{array}{cc}-1&-1\\0&1\end{array}\right] ) + 0*det(\left[\begin{array}{cc}-1&s\\0&-1\end{array}\right] )\\\\= s(s(1)-(-1*-1)) - (-1)(-1*1 - (-1*0)) + 0\\= s(s - 1)) + 1(-1 + 0) \\=s^{2} -s-1

Equating the determinant to zero

s^{2} -s-1 =0\\

s = \frac{1}{2} * (1 ±5 )

s = 1.61 or -0.61

5 0
3 years ago
Consider a set of one-dimensional points: 6, 12, 18, 24, 30, 42, 48.
Vinvika [58]

Answer:

1) With initial centroids 10-40, final clusters are

first cluster (6,12,18,24,30)

second cluster (42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 378

2) With initial centroids 10-20, final clusters are

first cluster (6,12,18,24)  

second cluster (30,42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 348

Step-by-step explanation:

K-means works as follows

  • the points will be clustered according to their distance to the centroids.
  • Then centroids are updated as the cluster means.
  • This process continues until clusters doesn't change anymore

1)  <u><em>initial centroids</em></u> 10-40

first cluster (6,12,18,24)  mean:15

second cluster (30,42,48) mean:40

<u><em>new centroids</em></u> 15-40

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

<u><em>final centroids</em></u> 18-45

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

Sum of Squared errors = (18-6)^{2}+(18-12)^{2}+(18-18)^{2}+(18-24)^{2}+(18-30)^{2}+(45-42)^{2}+(45-48)^{2}=378

2)<u><em>initial centroids</em></u> 10-20

first cluster (6,12)  mean:9

second cluster (18,24,30,42,48)  mean:32.4

<u><em>new centroids</em></u> 9-32.4

first cluster (6,12,18) mean:12

second cluster (24,30,42,48) mean:36

<u><em>new centroids</em></u> 12-36

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

<u><em>final centroids</em></u> 15-40

first cluster (6,12,18,24) mean:15  

second cluster (30,42,48) mean:40

Sum of Squared errors = (15-6)^{2}+(15-12)^{2}+(15-18)^{2}+(15-24)^{2}+(40-30)^{2}+(40-42)^{2}+(40-48)^{2}=348

6 0
3 years ago
Is 6 a factor of 81 yes or no
topjm [15]
To test whether it's a factor:

-- Divide the big number by it.                  81 / 6  =  13.5 .

-- If the quotient is a whole number,
   then the small number is a factor
   of the big number.                                  13.5 is not a whole number.

-- If the quotient is not a whole number,
   then the small number is NOT a factor
   of the big number.                                        6 is NOT a factor of 81 .

8 0
3 years ago
Read 2 more answers
Plz help i don't understand
gayaneshka [121]
How can i help you?
I would love to help you

4 0
3 years ago
1. A room is in the shape of a rectangle. The width of the room is 2 feet longer than two thirds the length. If the room is 33 f
morpeh [17]
2/3 of 33 is 22
so 22 +2 = 24
so 24x33=792
so the area is 792
7 0
4 years ago
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