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Neko [114]
3 years ago
10

4x + 2 3x+24 solve for x

Mathematics
1 answer:
Nady [450]3 years ago
8 0

Answer:

x=22

Step-by-step explanation:

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
Point G is on line segment FH. Given FH = 5x + 2, GH = 5x – 9, and
Anni [7]

Answer:

Step-by-step explanation:

11

6 0
3 years ago
Question 8 of 10
Sliva [168]

Answer:

y = (-3/7)x + 2

Step-by-step explanation:

slope-intercept form is y = mx + b, where m = slope and b = y-intercept.

all you need to do is plug the values into the equation! :)

since your slope is (-3/7), plug that in for m.

y = mx + b ⇒ y = (-3/7)x + b

and since your y-intercept is 2, plug that in for b.

y = (-3/7)x + b ⇒ y = (-3/7)x + 2

therefore, the line's equation in slope-intercept form is y = (-3/7)x + 2.

<em>don't worry about the parentheses, i only put them in there to separate the 7 in -3/7 from x. i'm not good at putting equations in here on brainly lol i just wanted to make sure you didn't think that it was -3 over 7x.</em>

<em />

i hope this helps! have a lovely day <3

5 0
2 years ago
Read 2 more answers
Simplify this expression 3+2(2p+4t)+6+5p
Licemer1 [7]
3+4p+8t+6+5p
9+9p+8t
......
3 0
3 years ago
Operations absolute value <br><br>|4 - 9| =<br><br>|4| -9 =
Lelu [443]
|4-9|
|-5|
5

|4|-9
4-9
-5

absolute value is the numbers distance from zero
6 0
2 years ago
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