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3 years ago

How does the definition of percent help you write fraction and decimal equivalent

Mathematics

1 answer:

irakobra [83]3 years ago

4 0

It helps by giving you a hint as to what the fraction or decimal may be. Ex. 30%, 0.3, 3/10

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

2 years ago

Solve each system by elimination 5x+y=9 10x-7y=-18 -4x+9y=9 x-3y=-6

tiny-mole [99]

5x + y = 9....multiply by 7
10x - 7y = -18
----------------
35x + 7y = 63 (result of multiplying by 7)
10x - 7y = -18
----------------add
45x = 45
x = 45/45
x = 1

5x + y = 9
5(1) + y = 9
5 + y = 9
y = 9 - 5
y = 4

solution is : (1,4)
=========================
-4x + 9y = 9
x - 3y = -6 ....multiply by 4
----------------
-4x + 9y = 9
4x - 12y = -24 (result of multiplying by 4)
---------------add
- 3y = - 15
y = -15/-3
y = 5

x - 3y = -6
x - 3(5) = -6
x - 15 = -6
x = -6 + 15
x = 9

solution is : (9,5)

3 0

3 years ago

Graph the functions f(x)=−6x+2 and g(x)=−2x+2+6 on the same coordinate plane.

mr Goodwill [35]

Answer:

here

Step-by-step explanation:

3 0

3 years ago

Please help with this area

agasfer [191]

Answer:

L = 7 W= 12

Step-by-step explanation:

Ok so we already know that a rectangle is not even so the numbers will have to be 2 diff numbers.

The length is 5 feet less then width

w*l= 84

1* 84 2* 41 3*28 4*21 6*14 7*12

84-1 41-2 28-3 21-4 14-6 12-7

83 39 25 19 8 5

So,

your equation would be l*w = 7*12

7 0

2 years ago

What is 45x3,679= what is the sum

Westkost [7]

Answer:

679

Step-by-step explanation:

5 0

2 years ago