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Naily [24]
3 years ago
12

Show in fact that 1=9m + 20n for some integers m and n

Mathematics
1 answer:
marta [7]3 years ago
5 0

Answer:

1=9\cdot 9+20\cdpt (-4)=81-80

Step-by-step explanation:

The greatest common divisor between 9 and 20 is 1, so we know the equation 1=9m+20n has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.

By inspection we just list some multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

and also list some mutiples of 20:

20, 40, 60, 80, 100, 120

And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.

For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:

20 = 9 * 2 + 2

Then we divide 9 by the remainder we got, which is 2:

9 =  2 * 4 + 1

we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:

9 - 2*4 = 1

And then we solve for 2 from the first equation, and plug that in into the previous equation:

20 - 9*2 =2

9 - ( 20 - 9*2)*4 = 1

which does give us the same solution: 9\cdot 9 +20\cdot (-4)=1

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The <span>principle that helps us to determine the total number of outcomes in a sample space is the counting principle.

</span>The Fundamental Counting Principle: If there are “a” ways for one event to happen, and “b” ways for a second event to happen, then there are “a * b” ways for both events to happen.
7 0
3 years ago
A line passes through the two points (-4,6) and (2,-5). Calculate the following parts:
Viktor [21]

A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.

<h3>What is the slope of a line which passes through points ( p,q) and (x,y)?</h3>

Its slope would be:

m = \dfrac{y-q}{x-p}

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope m of the line is given as

m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}

The equation of a line is  

( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6}  (x+4)\\\\6( y -6) = (-11)  (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0

Hence, the equation is  11x +6y - 80 = 0

Learn more about slopes here:

brainly.com/question/2503591

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8 0
2 years ago
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate is possible, he will travel ____ miles in 8 h
spayn [35]

Answer:

520 miles

Step-by-step explanation:

since 4 is half of 8, you just multiply 260 by 2.

4 0
3 years ago
Read 2 more answers
Help me!!!!!!! BONUS POINTS!!!!!!!!!!!!!!
choli [55]

Answer: -10x (5x^3 - 8x^2 - 3x - 9) is the factored solution.

6 0
3 years ago
Read 2 more answers
Help is appreciated! Thanks!
sukhopar [10]

Answer:

  1. 16√3
  2. -45+15i
  3. √255
  4. 6√2 +3√10

Step-by-step explanation:

1)

-4i\sqrt{-48}=-4i\sqrt{(-1)(4^2)(3)}=(-4i)(4i)\sqrt{3}=16\sqrt{3}

__

2)

(-5-5i)(3-6i)=-5(3-6i)-5i(3-6i)=-15+30i-15i+30i^2=-15-30+15i\\\\=-45+15i

__

3)

\sqrt{3}\sqrt{5}\sqrt{17}=\sqrt{3\cdot 5\cdot 17}=\sqrt{255}

__

4)

\sqrt{3}(\sqrt{24}+\sqrt{30})=\sqrt{3\cdot 24}+\sqrt{3\cdot 30}=\sqrt{6^2\cdot 2}+\sqrt{3^2\cdot 10}\\\\=6\sqrt{2}+3\sqrt{10}

_____

The applicable identities are ...

\sqrt{a^2b}=a\sqrt{b}\\\\i^2=-1

7 0
3 years ago
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