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Neporo4naja [7]
3 years ago
15

Find the lengths of the sides of the triangle if the vertices of EFG are E(-2,-3), F(-2,2) and G(3,2). Find the lengths of FG

Mathematics
1 answer:
krek1111 [17]3 years ago
3 0

Answer:

FG=5

Step-by-step explanation:

Use distance formula FG=√(3+2)² +(2-2)²=√25=5

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Let $s$ be a subset of $\{1, 2, 3, \dots, 100\}$, containing $50$ elements. how many such sets have the property that every pair
Tamiku [17]

Let A be the set {1, 2, 3, 4, 5, ...., 99, 100}.

The set of Odd numbers O = {1, 3, 5, 7, ...97, 99}, among these the odd primes are :

P={3, 5, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

we can count that n(O)=50 and n(P)=24.

 

 

Any prime number has a common factor >1 with only multiples of itself.

For example 41 has a common multiple >1 with 41*2=82, 41*3=123, which is out of the list and so on...

For example consider the prime 13, it has common multiples >1 with 26, 39, 52, 65, 78, 91, and 104... which is out of the list.

Similarly, for the smallest odd prime, 3, we see that we are soon out of the list:

3, 3*2=6, 3*3=9, ......3*33=99, 3*34=102.. 

we cannot include any non-multiple of 3 in a list containing 3. We cannot include for example 5, as the greatest common factor of 3 and 5 is 1.

This means that none of the odd numbers can be contained in the described subsets.

 

 

Now consider the remaining 26 odd numbers:

{1, 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99}

which can be written in terms of their prime factors as:

{1, 3*3, 3*5, 3*7, 5*5,3*3*3, 3*11,5*7, 3*13, 2*2*3*3, 7*7, 3*17, 5*11 , 3*19,3*21, 5*13, 3*23,3*5*5, 7*11, 3*3*3*3, 5*17, 3*29, 7*13, 3*31, 5*19, 3*3*11}

 

1 certainly cannot be in the sets, as its common factor with any of the other numbers is 1.

3*3 has 3 as its least factor (except 1), so numbers with common factors greater than 1, must be multiples of 3. We already tried and found out that there cannot be produced enough such numbers within the set { 1, 2, 3, ...}

 

3*5: numbers with common factors >1, with 3*5 must be 

either multiples of 3: 3, 3*2, 3*3, ...3*33 (32 of them)

either multiples of 5: 5, 5*2, ...5*20 (19 of them)

or of both : 15, 15*2, 15*3, 15*4, 15*5, 15*6 (6 of them)

 

we may ask "why not add the multiples of 3 and of 5", we have 32+19=51, which seems to work.

The reason is that some of these 32 and 19 are common, so we do not have 51, and more important, some of these numbers do not have a common factor >1:

for example: 3*33 and 5*20

so the largest number we can get is to count the multiples of the smallest factor, which is 3 in our case.

 

By this reasoning, it is clear that we cannot construct a set of 50 elements from {1, 2, 3, ....}  containing any of the above odd numbers, such that the common factor of any 2 elements of this set is >1.

 

What is left, is the very first (and only) obvious set: {2, 4, 6, 8, ...., 48, 50}

 

<span>Answer: only 1: the set {2, 4, 6, …100}</span>

8 0
3 years ago
What is 5/20 simplified ?
andre [41]

5/20 simplified is 1/10

it's simple math

5 0
3 years ago
Read 2 more answers
A student survey was conducted in a major university, where data were collected from a random sample of 750 undergraduate studen
Mekhanik [1.2K]

Answer:

Pie Chart

Step-by-step explanation:

The variable mentioned in this case is categorical. That is, it has no numerical value, and can only be put into categories.

Some of the basic rule In statistics to represent data using charts are as follows:

• For categorical variables (nominal/ordinal) variables, use pie charts and bar charts

• For interval/ratio variables, use histograms

A pie chart is a circular chart divided into wedge-like portions and is basically used to display percentage or proportion of categories in the data The percentage represented by each category is shown by the corresponding slice/portion of the whole pie.

4 0
3 years ago
F(x) = -3 +3
Mila [183]

Answer: Y

Step-by-step explanation:

Since f(x) passes through (0,3), its inverse should pass through (3,0).

  • This eliminates X and Z.

Also, since f(x) has a negative slope, so its inverse should also have a negative slope.

  • This eliminates W.
3 0
2 years ago
What is pie minus 6 plus 50<br>​
Natasha_Volkova [10]

Answer:

pie is about 3.14

3.14 - 6 = -2.86

-2.86 + 50 = 47.14

<em><u>47.14</u></em>

Step-by-step explanation:

7 0
2 years ago
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