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tatuchka [14]
2 years ago
11

Question: determine all solutions to the diophantine equation 3x + 7y = 4

Mathematics
1 answer:
yKpoI14uk [10]2 years ago
3 0
The difference between the coefficients 7 and 3 is 4, so one solution is
  y = 1, x = -1.
Then the remaining solutions will be of the form
  x = -7n-1
  y = 3n+1
for some integer n.


_____
Some of the solutions are (for n=0, -1, -2, 1, 2)
(x, y) = (-1, 1), (6, -2), (13, -5), (-8, 4), (-15, 7)
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Which equations support the fact that rational numbers are closed under subtraction?
Illusion [34]

Answer:

A rational number is said to be closed if the subtracted values and the result obtained are rational. Hence, the equations which supports the condition are :

5.5 - 0.5 = 4

5√4 - √4 = 4√4

Step-by-step explanation:

A.)

√8 - √8 = 0 ; the added values aren't rational and the result, Zero is not rational either.

B.)

5√4 - √4 = 4√4

5(2) - 2 = 2(2)

10 - 2 = 4

All the values in the expression are rational ; hence, it supports the assertion.

C)

5.5 - 0.5 = 4 ; all the values in the expression are rational, hence, it supports the fact.

2√3 - √3 = √3 ; the values in the expression are not rational, hence, it does not meet the condition.

Therefore, only options B and C supports the assertion.

Let me add that I learned most of this from Brainly a user named fichoh :)

7 0
2 years ago
The door code to gain access to a top-secret laboratory is 6 digits. The first 3 digits of the code are all odd, and the last 3
WINSTONCH [101]
5 odd numbers and 5 even numbers
since they can be repeated
5*5*5=first 3 digits
5*5*5=last 3 digits
in all
5*5*5*5*5*5=15625 ways
3 0
2 years ago
HELP ME OUT PLEASE!!! <br><br>What is the equation of this line?​
Verdich [7]

Answer: THe Second answer is the correct one

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey pa
PSYCHO15rus [73]

Answer:

A) \dfrac{11}{23}

B) \dfrac{88}{345}

Step-by-step explanation:

A survey of 46 college athletes found that

  • 24 played volleyball,
  • 22 played basketball.

A) If we pick one athlete survey participant at random,  the probability they play basketball is

P_1=\dfrac{22}{46}=\dfrac{11}{23}

B) If we pick 2 athletes at random (without replacement),

  • the probability we get one volleyball player is \dfrac{24}{46}=\dfrac{12}{23};
  • the probability we get another basketball player is \dfrac{22}{45} (only 45 athletes left).

Thus, the probability we get one volleyball player and one basketball player is

P_2=\dfrac{12}{23}\cdot \dfrac{22}{45}=\dfrac{88}{345}

5 0
3 years ago
On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three
igor_vitrenko [27]
Answer: 143 hamburgers and 429 cheese burgers

Explanation:

Call h and c the number of both items.
(h-hamburger and c-cheeseburger)

h + c = 572
c = 3h

Sub the second into the first

h + 3h = 572
4h = 572

Divide both sides by 4
h = 143 hamburgers

Use this back into the second equation
c = 3 • 143 = 429 cheeseburgers

3 0
3 years ago
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