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hram777 [196]
3 years ago
9

For any neZ^+, prove that the integers 8n +3 and 5n+2 are relatively prime. Compute the multipliers to compute inverse of one nu

mber with respect to the other number.
Mathematics
1 answer:
balandron [24]3 years ago
6 0

Answer:

See step-by-step explanation below

Step-by-step explanation:

This problem is solved using the Euclidean algorithm; to prove that the integers 8n + 3 and 5n + 2 are relative prime we have to prove that:

gcd(8n + 3, 5n + 2) = 1

gcd (8n + 3, 5n + 2) = gcd (3n + 1, 5n + 2) = gcd (3n + 1, 2n + 1) = gcd(n, 2n + 1) = gcd(n,1) = 1

⇒gcd(8n + 3, 5n + 2) = 1

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Jenny has 12 marbles.
gogolik [260]

Answer:

720g is your answer friend.

Step-by-step explanation:

  • The total weight of large marbles = 6×70=420g
  • The total weight of small marbles = 6×50=300g
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3 years ago
(Problem in two-dimensions.) Given the line: L1 : y = 2x , (2) find the equation of the line L2 perpendicular to L1 passing thro
kirill115 [55]

Given :

Equation of line 1 , y = 2x .

A point (1 , 2) .

To Find :

The equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) .

Solution :

Let , equation of line 2 is :

y = mx + c     .....eq 1 ( here , m is slope and c is a constant )

Now , we know when two lines are perpendicular product of their slope is -1 .

Slope of given line is 2 .

Therefore ,

2m=-1\\\\m=\dfrac{-1}{2}

Now putting value of m in equation 1 , we get :

y=\dfrac{-1}{2}x+c

Now , it is given that this point (1,2) satisfy the above equation .

So ,

2=\dfrac{-1}{2}(1)+c\\\\c=\dfrac{5}{2}

Putting value of c in above equation , we get :

y=-\dfrac{1}{2}x+\dfrac{5}{2}\\\\2y=-x+5

Therefore , the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) is 2y = -x +5 .

Hence , this is the required solution.

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4 years ago
What is the measure of the other acute angle ?
Vaselesa [24]

Answer:

62^{o}

Step-by-step explanation:

All the angles in a triangle add up to 180^{o}

Every right angle triangle has a right angle in it which is 90^{o}

So to find the remaining angle, you do 180^{o} - 90^{o} - 28^{o} = 62^{o}

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ella [17]

Answer:

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Step-by-step explanation:

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2 years ago
Ten frequent gamers are randomly selected. The random variable represents the number of frequent gamers who play video games on
notsponge [240]

Answer:

For this to be a binomial experiment, the assumption that is made is:

C. The probability of being selected is the same for all ten gamers.

Step-by-step explanation:

a) A binomial experiment must meet the following four conditions:

1. The experiment must consist of 'n' identical trials.

2. Each experiment must result in one of the two outcomes of either success or failure.

3. The probability of success (p) must remain the same from one experiment to the next.

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3 years ago
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