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Allisa [31]
3 years ago
5

Solve each equation for xx. For each step, describe the operation used to convert the equation. How do you know that the initial

equation and the final equation have the same solution set?
a. 1/5[10−5(x−2)]=1/10(x+1)
b. x(5+x)=x²+3x+1
c. 2x(x²−2)+7x=9x+2x³
Mathematics
1 answer:
ladessa [460]3 years ago
4 0

Answer:

a. x=1.8?

Step-by-step explanation:

im not really sure but i need help also. Im sorry but i just thought to say something.

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Jim says that the square root of 200 is between 14 and 15. Do you think that is reasonable? Without using a calculator, can you
sleet_krkn [62]

Answer:

the answer is 14.14

Step-by-step explanation:

4 0
2 years ago
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
2 + 3 × (8 + 53 ÷ 1)<br><br> Can please include the working to it. Thank you,
luda_lava [24]

Step-by-step explanation:

2 + 3 × (8 + 53 ÷ 1)

we first work out the equation in the brackets

so...

(8 + 53 ÷ 1)

division comes first so we divide 53÷1 which is 1 so the equation looks like this:

(8+53)

we work this out and get

61

then we work the rest out

2 + 3 × <u>61</u>

multiplication comes first so...

3×61= 183

and

2+ 183= 185

Therefore 2 + 3 × (8 + 53 ÷ 1)= <u>185</u>

Hope this helped- have a good day bro cya)

6 0
2 years ago
Read 2 more answers
Justin was looking for a birthday card for his sister. There were 9 funny cards, 7 serious cards, and 5 musical cards. How many
madam [21]
Just add.  7 + 9 + 5 = 21  So the answer is A.21
5 0
3 years ago
Read 2 more answers
What is 11=m-2 equal when your solving and checking your answer
AfilCa [17]
Add 2 to both sides

11+2 = 13

m=13
4 0
3 years ago
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