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ale4655 [162]
3 years ago
9

Mixed fractions: What is the value of 2 1/3 + 6 3/5 *

Mathematics
1 answer:
Studentka2010 [4]3 years ago
3 0

Answer:

134/15 or

8 14/15

Step-by-step explanation:

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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
Which addition sentences show you how to find 16-9?
Valentin [98]
This dosent make sense and where are the sentences ;-;
5 0
3 years ago
How to find the least common denominator with fractions?
Scrat [10]
Find out what the lowest number is that each of the numbers on the bottom of the fractions can divide into evenly.
3 0
3 years ago
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Write an equation of the line with the given slope that contains the given point.
Alchen [17]

Answer:

y=-2x+12

Step-by-step explanation:

We can use the point-slope form given by:

y-y_1=m(x-x_1)

Where <em>m</em> is the slope and (x₁, y₁) is a point.

So, we will substitute -2 for <em>m</em> and (5, 2) for (x₁, y₁). This gives us:

y-(2)=-2(x-(5))

Simplify:

y-2=-2(x-5)

Distribute:

y-2=-2x+10

Add 2 to both sides. Hence, our equation is:

y=-2x+12

3 0
3 years ago
2 Points
SOVA2 [1]

A

distributive property

-4x - y + 2x - 6y

Combine like terms

-2x - 7y

6 0
3 years ago
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