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Nataliya [291]
3 years ago
14

Please help and hurry

Mathematics
1 answer:
Crank3 years ago
8 0

Answer:

3,2

Step-by-step explanation:

Mind maps are a great way of

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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
3 years ago
A triangle has sides with lengths of 5 millimeters, 12 millimeters, and 14 millimeters. Is it a right triangle?
dmitriy555 [2]

PFA FOR THE ANSWER. YOU CAN USE THE PYTHAGOREAN EQUATION (I.E a2 + b2 =

3 0
3 years ago
Someone please help me with this math question!
stepladder [879]
1.25x + 2.5 \ \textless \  2.75x - 6.5 \\ \\ 2.5 \ \textless \  2.75x - 6.5 - 1.25x \ / \ subtract \ 1.25x \ both \ sides \\ \\ 2.5 \ \textless \  1.5x - 6.5 \ / \ simplify \\ \\ 2.5 + 6.5 \ \textless \  1.5x \ / \ add \ 6.5 \ both \ sides \\ \\ 9 \ \textless \  1.5x \ / \ simplify \\ \\ 6 \ \textless \  x \ / \ divide \ both \ sides \ 1.5 \\ \\ x \ \textgreater \  6 \ / \ change \ sides \\ \\ Answer: x \ \textgreater \  6 (A)
8 0
3 years ago
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What is the value of d to the nearest tenth?
Ghella [55]

Answer: d=13.8

Step-by-step explanation:

A line that cuts a circle at two points is called "secant".

There is a theorem known as "Intersecting Secant Theorem". This is the theorem you need to use to find the value of "d".

According the Intersecting Secant Theorem:

(14)(14+20)=(16)(16+d)\\(14)(34)=(16)(16+d)

Having this expression, the next step is to solve for "d":

Use Distributive property:

476=256+16d

Subtract 256 from both sides:

476-256=-256+256+16d

220=16d

Divide both sides by 16:

\frac{220}{16}=\frac{16d}{16}\\\\13.75=d

The value of "d" rounded to the nearest tenth is:

d=13.8

6 0
3 years ago
What two factors of 25 also have the sum of -10?
Andrews [41]

Answer:

-5 and -5.

Step-by-step explanation:

Two negative numbers multiply to make a positive and add to make a negative.

4 0
2 years ago
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