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densk [106]
1 year ago
15

Triangle KML and triangle PRQ are shown in the figure belowK404008 cms4 cms10 cmsOL3 cms6 cmsRM17) Are these triangles similar?1

8) Are these triangles congruent?

Mathematics
1 answer:
s2008m [1.1K]1 year ago
8 0

Two triangles are similar if the only difference between them is the size, this means that their internal angles must be the same. If we look at the picture the first triangle has one angle equal to 40 degrees, one equal to 80 degrees and the third one is unkown (x). The second triangle has one angle equal to 40 degrees, one equal to 60 degrees and the third one is unkown (y). The sum of the internal angles of a triangle must be equal to 180 degrees, with this information we can find the values of the missing angles. We have:

\begin{gathered} 40+80+x=180 \\ 120+x\text{ = 180} \\ x\text{ = 180-120=60} \end{gathered}\begin{gathered} 40+60+y=180 \\ 100+y=180 \\ y=180-100=80 \end{gathered}

Therefore the internal angles of the first triangle are (40,80,60) and the angles of the second triangle are (40,80,60) as well, therefore they are similar.

Two triangles are congruent if they have sides with the same length. Which is not the case, because the sides of one triangle is (8, 10, 6) while the other is (4,3 and unkown). Therefore they are not congruent.

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Answer:

C. The distribution for town A is symmetric, but the distribution for

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Step-by-step Explanation:

From the box plots attached in the diagram below, which shows data of low temperatures for town A and town B for some days, we can compare the shapes of the box plot by visually analysing both box plots and how the data for each town is distributed.

=> For town A, the shape of the box plot is symmetric because both quartiles seem equal, and the median also divides the rectangular box into two equal halves. Both whiskers also appear to be of equal lengths.

The box plot for Town A takes a symmetric shape, and this shows a typical normal distribution of data.

=> On the other hand, Town B data distribution is different. The median seem close to the top half of the box and does not divide the box into equal halves. This shows the distribution is skewed. Since the whisker is shorter from the upper end of the box to the left side, we can infer that the distribution for Town B is skewed to the left, and it is negatively skewed.

=> The right comparison of the shapes of the box plots is "C. The distribution for town A is symmetric, but the distribution for town B is negatively skewed."

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HELP ASAP PLEASE
Roman55 [17]

Answer:

a. median is 8

b. first quartile is 7

c. third quartile is 9.5

d. below

e. below

Step-by-step explanation:

7, 10, 10, 6, 7, 8, 8, 7, 9.

Place number in order least to greatest

6, 7, 7, 7, 8, 8, 9, 10, 10

a. What is the median?

The median is the middle number in a data set

number of terms in data set (n) + 1 / 2 =

9 + 1 / 2 = 10 / 2

<u>6, 7, 7, 7,</u> 8, <u>8, 9, 10, 10</u>

The median is 8

b. What is the first quartile?

Q1 is the central point between the smallest score and the median

<u>6,</u> 7, 7<u>, 7 </u>

since there is even number of data points you find the average,

7 + 7 / 2 = 14 / 2 = 7

c. What is the third quartile?

Q3 is the central point between the median and the largest score

<u>8</u>, 9, 10, <u>10</u>

since there is even number of data points you find the average,

9 + 10 / 2 = 19 / 2 = 9.5

d. Draw a box plot of the data.

below

e. Write two conclusions about the data shown in the box plot.

There are no outliers with a minimum of 6 and a maximum of 10. The Interquartile Range is 2.5 (9.5 - 7)

3 0
2 years ago
I got 47.01816163 metres. When I tried to round it I got it wrong. Can someone please help me?
DerKrebs [107]

Answer:

28 m

Step-by-step explanation:

The top angle in the triangle = 90° - 62° = 28°

Using the cosine ratio in the right triangle

cos28° = \frac{adjacent}{hypotenuse} = \frac{25}{x}

cross- multiply

x × cos28° = 25 ( divide both sides by cos28° )

x = \frac{25}{cos28} = 28.31425... ≈ 28 m

Thus the distance from the top to the crocodile is 28 m

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