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Anit [1.1K]
3 years ago
12

Write 1-2log7x as a single logarithm

Mathematics
1 answer:
slavikrds [6]3 years ago
4 0

Answer:

log_{7} \frac{7}{x^{2} }

Step-by-step explanation:

We need to write 1 - 2log_{7}x as a single logarithm.

We know that

log_{7}7 = 1

Therefore we have:

log_{7}7 - 2log_{7}x

→ log_{7}7 - log_{7}x^{2}

→ log_{7} \frac{7}{x^{2} }

The solution is: log_{7} \frac{7}{x^{2} }

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Thank you to whoever helps!
shepuryov [24]

Answer:

  • M
  • 90°

Step-by-step explanation:

The segment joining an original point with its rotated image forms a chord of the circle of rotation containing those two points. The center of the circle is the center of rotation.

This means you can find the center of rotation by considering the perpendicular bisectors of the segments joining points with their images. Here, the only proposed center that is anywhere near the perpendicular bisector of DE is point M.

__

Segment AD is perpendicular to corresponding segment FE, so the angle of rotation is 90°. (We don't know which way (CW or CCW) unless we make an assumption about which is the original figure.)

4 0
3 years ago
Find the point on the sphere closest to the plane
Ratling [72]
Use the concept of Lagrange multipliers.
3 0
3 years ago
Consider the two data sets below:
alina1380 [7]

Answer:

<u><em>Option c) The data sets will have the same values of their interquartile range.</em></u>

<u><em></em></u>

Explanation:

<u>1. The values are in order: </u>they are in increasing oder, from lowest to highest value.

<u>2. Calculate the interquartile range.</u>

<em />

<em>Interquartile range</em>, IQR, is the third quartile, Q3, less the first quartile Q1:

  • IQR = Q3 - Q1

To find the first and the third quartile, first find the median:

<u>Data Set 1</u>: 19, 25, 35, 38, 41, 49, 50, 52, 59

             [19, 25, 35, 38],  41,  [49, 50, 52, 59]

                                         ↑

                                     median = 41

   

<u>Data Set 2</u>: 19, 25, 35, 38, 41, 49, 50, 52, 99

             [19, 25, 35, 38] , 41,  [49, 50, 52, 99]

                                         ↑

                                      median = 41

Now find the median of each subset: the values below the median and the values above the median.

Data set 1: <u>First quartile</u>

                [19, 25, 35, 38],

                            ↑

                           Q1 = [25 + 35] / 2 = 30

                   <u>Third quartile</u>

                   [49, 50, 52, 59]

                                ↑

                                Q3 = [50 + 52] / 2 = 51

                     IQR = Q3 - Q1 = 51 - 30 = 21

Data set 2: <u> First quartile</u>

                   [19, 25, 35, 38]

                               ↑

                               Q1 = [25 + 35] / 2= 30

                  <u>Third quartile</u>

                   [49, 50, 52, 99]

                                ↑

                                Q3 = [52 + 50]/2 = 51

                   IQR = 51 - 30 = 21

Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)

This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.

<em>An outlier will change the range</em> because the range is the maximum value less the minimum value.

5 0
3 years ago
Is x = 12 a solution to the equation 6 + x = 19
gladu [14]

Answer:

Incorrect.

Step-by-step explanation:

6 + x = 19

Plug in when x = 12

6 + 12 = 19

18 = 19

It is incorrect, so 12 is not a solution.

7 0
3 years ago
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iogann1982 [59]

Answer: The answer is b !

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