Triangle inequality theorem

Answers

Answer 1

Answer:

The triangle inequality theorem is an important part of geometry in order to mention the dimension of the sides of a triangle clearly.

What is triangle inequality theorem?

The triangle inequality theorem states that, the sum of the length of two sides must be greater than the length of the third side of that triangle.

Here, three sides of this triangle ABC are AB, BC, and CA.

Therefore, as per the triangle inequality theorem:

(Length of AB + length of BC) must be greater than the length of CA.

Therefore, (AB + BC) > CA.

(Length of BC + length of CA) must be greater than the length of AB.

Therefore, (BC + CA) > AB.

(Length of AB + length of CA) must be greater than the length of BC.

Therefore, (AB + CA) > BC

For an example, if we are running in a triangular shaped track, then it can be easily understandable.

Now, if we start running from the point A, then to reach the point B the shortest path will be the straight line AB.

Instead of that, if we go to the C point at first and then reach the point B, then we will travel more distance.

Similarly, starting from the other points, we will get the same results.

Learn more about triangular inequality theorem here: brainly.com/question/18345497

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Answer 2

Answer: Triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side because if not you don't have a triangle.

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Greg was adding numbers on a number line. He started on –5 and then he added –8. Greg wrote that the answer was +13. Is Greg's answer reasonable? A. No, it is not reasonable because –5 + –8 = –13. B. Yes, it is reasonable because –5 + –8 = +13. C. No, it is not reasonable because if you add two numbers you will get a number that is greater than either of the two numbers.

Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth. 27,16,8,5,19,14,22,31,13,5,23,16,8

Answers

Answer:

Hence,

Mean=15.9

Median=16

Interquartile=14.5

Step-by-step explanation:

On arranging our data in the increasing order we get the data set as:

5 5 8 8 13 14 16 16 19 22 23 27 31

Now we find the mean as:

$Mean=(5+5+8+8+13+14+16+16+19+22+23+27+31)/(13)\n\nMean=(207)/(13)\n\nMean=15.92$

Now, we know that the median is the central tendency of the data and lie in the middle of the data.

Hence, by looking at the data we see that the middle value of the data is 16.

Hence, Median=16.

Now, the lower set of data is:

5 5 8 8 13 14

Now, the lower quartile is calculated as:

The middle value of the lower set of data is:

8 8

Hence, the lower quartile $]Q_1$ is middle of 8,8.

i.e. $(8+8)/(2)=8$

similarly the upper set of data is:

16 19 22 23 27 31.

Similarly the upper quartile is calculated as:

$Q_3=(22+23)/(2)=22.5$

Hence, interquartile range (IQR) is calculated as:

$Q_3-Q_1=22.5-8=14.5$

Hence,

Mean=15.9

Median=16

Interquartile=14.5

The mean is 15.92, the median is 16, and the interquartile range is 14.5

The polynomial y = x2 + 6x + 9 has a repeated factor. (It may help to graph the equation.) A.True B.False

Answers

For the answer to the question above asking if it is true or false that The polynomial y = x2 + 6x + 9 has a repeated factor.
The answer to this question is true and that would be 3
(x+3)(x+3)
I hope my answer helped you.

B1 of a trapezoid in which Area = (48x+68) inch squared, Height = 8 in, B2 = (9x + 12) in.what I have so far is

48x +68 = 8 (B1 + 9x +12)

what do I do from there????????????????? the question is asking to solve for Base 1/ B1

Answers

A=(1/2)(b1+b2)h =

=(48x+68)in² = (1/2)( b1+(9x+12))8

=b1= 3x+5

Which of the following is the solution to (x-13)<18

Answers

Answer:

The solution to the equation (x-13)<18 is that x can be equal to the numbers 0-17 (NOT including negative numbers)

If a line passes through the point (1,9) and has a slope of 6 , write it as an equation

Answers

$y= mx+b$

$y=6x+b$

$(9)=6(1)+b$

$9=6+b$

$3 = b$

$y=6x+3$

$y-y_1=m(x-x_1)\n y-9=6(x-1)\n y=6x-6+9\n y=6x+3$

The concert lasts 60 minutes, and the songs are all the same length. The choir sings a total of 12 songs, 2 of which are sung by the sopranos only. For how many minutes do the sopranos sing by themselves? Solve the equations using a letter for the unknown quantity.

Answers

60mins= 12x
60/12=12x/12
5=x
x= length of songs
5 x 2= 10 mins soprano sings by themselves

Answer:

10 minutes

Step-by-step explanation:

60 / 12 = 5

5 *2 = x=10

this means that x = 10

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