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Harman [31]
2 years ago
10

PLEASE ANSWER FAST!! THANK YOU :)

Mathematics
1 answer:
Makovka662 [10]2 years ago
3 0

Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

k^{3}+2k = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, (k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) 5^{2n}-1\\

n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24

This statement is also true

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Answer:

thursday cuz -25 is the lowest out of them

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2 years ago
A study found that there is no direct relationship between the time that 8th-grade students spend brushing their teeth and their
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c

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7 0
3 years ago
Help me out with number 8!!! I’m confused and I need this by tomorrow HELP PLEASE
ivann1987 [24]
We can use elimination for these set of systems.
First, we need to set up our variables.
Belts=b
Hats=h
Now, the situation is 6 belts and 8 hats for $140. The situation after is 9 belts and 6 hats for $132.
Let’s set up our system of equations.
6b+8h=140
9b+6h=132
We need to eliminate a variable. Since b has coefficients of 6 and 9, we can easily eliminate b by multiplying the top equation by 3 and the bottom by -2.
18b+24h=420
-18b-12h=-264
Now let’s add.
12h=156
Let’s divide to get h by itself.
156/12=13=h
So a hat costs $13. We need to put in 13 for one of the equations so we can find the cost of a belt.
9b+6(13)=132
9b+78=132
We need b by itself.
9b=54
54/9=6
Belts are $6
We can also use the first equation to check our answers.
6(6)+8(13)
36+104
140.
So, the price of a belt is $6 while the price of a hat is $13.
































3 0
2 years ago
Name the values Of the 4s in the number 400,440
gavmur [86]

The first value of 4 is in the tens place.

The second value of 4 is in the hundreds place.

The third value of 4 is in the hundred thousands place

40

400

400,000

6 0
2 years ago
Jeff provides photos for two online sites: site A and site B.
Setler [38]
$0.25 you just have to multiply .65 times 5 for site A which is $3.25 and for sure b just plug in 5 for x and multiply by .60 which gives you $3.00 so site A gives you $0.25 more
5 0
3 years ago
Read 2 more answers
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