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Ann [662]
3 years ago
10

Which of the following statements are always true?

Mathematics
2 answers:
Igoryamba3 years ago
4 0

Answer: A trapezoid is always a parallelogram.

Step-by-step explanation:

gogolik [260]3 years ago
4 0
Answer
the third one a trapezoid can always be a quadrilateral

hope this helps and have a wonderful day :)
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There are 8 tennis players in a round robin tournament, which means each team will play every other team once. How many matches
Aliun [14]
<h3>Answer:  28</h3>

==========================================================

Explanation:

Method 1

Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.

There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.

Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.

----------------------------------

Method 2

There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.

----------------------------------

Method 3

Use the nCr combination formula with n = 8 and r = 2

n C r = \frac{n!}{r!(n-r)!}\\\\8 C 2 = \frac{8!}{2!*(8-2)!}\\\\8 C 2 = \frac{8!}{2!*6!}\\\\8 C 2 = \frac{8*7*6!}{2!*6!}\\\\ 8 C 2 = \frac{8*7}{2!}\\\\ 8 C 2 = \frac{8*7}{2*1}\\\\ 8 C 2 = \frac{56}{2}\\\\ 8 C 2 = 28\\\\

There are 28 combinations possible. Order doesn't matter (eg: match-up AB is the same as match-up BA).

Notice how the (8*7)/2 expression is part of the steps shown above in the nCr formula.

7 0
2 years ago
How did the Romanov dynasty increase Russia's power?
Degger [83]

Answer:

Step-by-step explanation:

  1. The Romanov Dynasty (1613 to 1917) was the last imperial dynasty to rule Russia. During the Romanov reign Russia became and remained a major European power.
  2. The Romanovs share their origins with a handful of other Russian noble families. One of the ancestors of the world-renowned dynasty was Andrey Kobyla – a boyar who lived during the middle of the 14th century. Kobyla was documented in contemporary chronicles only once, in 1347, when he was said to have been sent to Tver with the purpose of meeting the daughter of Alexander I of Tver. Later generations assigned other more illustrious pedigrees to Kobyla, however, they are highly unlikely to be true.
  3. An 18th century genealogy chart even claimed that Kobyla was the son of the Prussian prince Glanda Kambila, who came to Russia in the second half of the 13th century, fleeing the invading Germans. Indeed, one of the leaders of the Prussian rebellion of 1260-1274 against the Teutonic order was named Glande, but the theory acquired no further proof.
  4. In another theory, which is more likely to be true even though it is less complementing, Kobyla's origins were not that spectacular – his relatives were nicknamed after horses and other house animals (“kobyla” means “mare” in Russian), thus suggesting his descent from one of the royal equerries.
  5. One of Kobyla's sons, Feodor, a boyar in the boyar Duma of Dmitry Donskoy, was nicknamed Koshka, or “cat.” His descendants took the surname Koshkin and then changed it to Zakharyin. Later the family split this surname into two branches: Zakharyin-Yakovlev and Zakharyin-Yuriev. During the reign of Ivan the Terrible, the former family became known as Yakovlev, whereas the grandchildren of Roman Zakharyin-Yuriev changed their name to Romanov.
  6. The Romanov Dynasty began with the election of Mikhail Romanov, a 16-year-old boyar, by the Zemsky Sobor, or Assembly of the Land – the first Russian parliament of the feudal estates type.
  7. Initially, Mikhail’s mother protested against the election of such a young and inexperienced man, but the boyars assured her that Mikhail would be held responsible to God for the destruction of Russia and other mortal sins if he persisted in his refusal to accept the title.
  8. When young Mikhail learned he was about to be granted the highest title anyone could dream of in Russia, he burst into tears of fear and despair. He was finally persuaded to accept the throne by his mother who saw no way out, so she blessed the young man who had to obey. Mikhail Romanov was crowned on 22 July 1613.
  9. The first member of the Romanov Dynasty and founder of the clan dedicated the time of his reign to reforms, thus changing the political situation that had formed by that time in ancient Russia.
  10. The first task of the new Tsar was to clear the land of the invaders infesting it – thus Sweden and Poland were dealt with respectively.

 

3 0
3 years ago
5. A soil sample has a ratio of nitrogen to calcium of 4:6. If
shusha [124]

I uploaded the answer to a file hosting. Here's link:

tinyurl.com/wpazsebu

4 0
3 years ago
The table below shows the surface area y in square inches, of a shrinking puddle in x hours
Kruka [31]
Part A
Correlation coefficient: -.99
This tells us that as time goes on (value of x increases) the area of the puddle goes down (value of y decreases)

Part B
y₂ - y₁
-------   = slope
x₂ - x₁
9 - 15
--------
5 - 8
-6/-3 = 2
So the slope equals -2, regardless of the fact that we got 2 as an answer there, we know that it is a negative slope 

Part C
The data represents causation because an increase in the value of x results in a decrease in the value of y, this shows an example of direct causation between x and y.
8 0
3 years ago
Read 2 more answers
What is 5 3/4 as a decimal?
ziro4ka [17]

Answer:

5.75

Step-by-step explanation:

5 \frac{3}{4}  =  \frac{5 \times 4 + 3}{4}  = \frac{20 + 3}{4}   =  \frac{23}{4}  = 5.75  \\

7 0
3 years ago
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