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alekssr [168]
3 years ago
9

Prove that every integer greater than 7 can be written by using 3's and 5's only. that is, for every n > 7 there exist non-ne

gative integers tn, sn such that n = 3tn + 5sn.
Mathematics
1 answer:
Taya2010 [7]3 years ago
4 0
An integer may be a multiple of 3.
An integer may be 1 greater than a multiple of 3.
An integer may be 2 greater than a multiple of 3.

It is redundant to say an integer is 3 greater than a multiple of 3 (that's just a multiple of 3, we've got it covered).  Same for 4, 5, 6, 7...

Let's consider a number which is a multiple of 3.  Clearly, we can write 3+3+3+3+... until we reach the number.  It can be written as only 3's.

Let's consider a number which is 2 greater than a multiple of 3.  If we subtract 5 from that number, it'll be a multiple of 3.  That means we can write the number as 5+3+3+3+3+...  Of course, the number must be at least 8.

Let's consider a number which is 1 greater than a multiple of 3.  If we subtract 5 from that number, it'll be 2 greater than a multiple of 3.  If we subtract another 5, it'll be a multiple of 3.  That means we can write the number as 5+5+3+3+3+3+...  Of course, the number must be at least 13.

That's it.  We considered all the numbers.  We forgot 9, 10, 11, and 12, but these are easy peasy.

Beautiful question.
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Which has the greatest value -10, -3, 6, 9
VMariaS [17]
9 has the greatest value because it’s positive
7 0
2 years ago
What is the value of the product (4 – 2i)(6 + 2i)? 20 – 4i 20 + 16i 28 + 16i 28 – 4i
Darya [45]

(4 – 2i)(6 + 2i)

FOIL

First : 4*6 =24

Outer: 4*2i = 8i

Inner: -2i* 6 = -12i

Last: -2i*2i = -4i^2 =-4(-1) =4

Add together

24+8i-12i+4

28-4i

Answer: 28-4i

8 0
3 years ago
Read 2 more answers
In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of
katovenus [111]

Answer:

sample mean

Step-by-step explanation:

6 0
3 years ago
Q: A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte.
DiKsa [7]

The linear equation which can be used to determine a user's monthly

bill is c = 60 + 0.05 d ⇒ D

Step-by-step explanation:

The given is:

  • A cell phone company charges $60.00 a month for up to 1 gigabyte of data
  • The cost of additional data is $0.05 per megabyte
  • d represents the number of additional megabytes used
  • c represents the total charges at the end of the month

We need to find which equation can be used to determine a user's monthly bill

The form of the linear equation is y = mx + b, where b is the constant amount and m is the rate of change

∵ The company charges $60.00 a month for up to 1 gigabyte of data

- That means it is a constant amount each month

∴ b = 60

∵ The cost of additional data is $0.05 per megabyte

- That means it depends on the number of additional megabyte,

   so it is not constant, it is the rate of change

∴ m = 0.05

∵ d represents the number of additional megabytes

∴ x = d

∵ c represents the total charges at the end of the month

∴ y = c

Substitute y by c, m by 0.05, x by d and b by 60 in the form of the linear equation above

∴ c = 0.05 d + 60

- We can rearrange the terms of the right hand side

∴ c = 60 + 0.05 d

The linear equation which can be used to determine a user's monthly

bill is c = 60 + 0.05 d

Learn more:

You can learn more about linear function in brainly.com/question/9801816

#LearnwithBrainly

7 0
3 years ago
Find x, round to the nearest tenth degree.
Romashka [77]

Answer:

Step-by-step explanation:

Use the Law of Cosines

A = arccos[(10²+14²-9.6²)/(2×10×14) ≅ 43.3°

5 0
3 years ago
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