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3 years ago

What are ratios that are equivalent to 16:12

Mathematics

2 answers:

Zepler [3.9K]3 years ago

6 0

Answer:

4:3, 8:6, 12:9, 20:15, 24:18, 28:21, 32:24, 36:27, 40:30 and so on.

Step-by-step explanation:

The denominators are all multiples of 3 and the numerators are multiples of 4.

Reil [10]3 years ago

3 0

Answer:

20:15, 24:18, 28:21, etc.

Step-by-step explanation:

Just divide 16 by 12 to get 4/3. Then whatever you multiply to 4, multiply to 3, and get more answers.

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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

The numbers below show a pattern 0.006 0.6 6

Ivenika [448]

Answer:

Yes

Step-by-step explanation:

The decimal points moves to the right at a constant pace.

0.006 -> 0.06 -> 0.6 -> 6

In other words, we are just multiplying each one by 10 to get the next value.

Best of Luck!

7 0

3 years ago

Which of the following lists of network types appears in decreasing order of size?

Tju [1.3M]

WAN, LAN, PAN

Wide Area Network, Local Area Network, Personal Area Network

6 0

3 years ago

Read 2 more answers

Write an equation for the description.<br> The difference between a number x and 19 is 27.

ra1l [238]

Answer

x-19=27

Step-by-step explanation:

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3 years ago

Which of the following is in Integrity but not a whole number A -9.6 B -4

abruzzese [7]

Answer:

B. -4.

Step-by-step explanation:

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