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Anton [14]
2 years ago
7

Prove by induction that 7^2n+1 +1 is divisible by 8, for all nEN

Mathematics
1 answer:
fredd [130]2 years ago
7 0

Answer:

See below.

Step-by-step explanation:

Base case:

Replace n with 1.

7^(2×1+1)+1

7^3+1

343+1

344

8 is a factor of 344 since 344=8(43).

Induction hypothesis:

Assume there is some integer n such that 7^(2k+1)+1=8n for positive integer k.

7^(2[k+1]+1)+1

7^(2k+3)+1

7^(2k+1+2)+1

7^(2k+1)7^2+1

49×7^(2k+1)+1

Induction step:

49×(8n-1)+1

49(8n)-49+1

49(8n)-48

8[49n-6]

This means 8 is a factor of 7^(2(k+1)+1)+1.

Thus, this proves for all positive integer n that 8 is a factor of 7^(2n+1)+1.

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The measure of a single angle of deviation on a regular octagon is 45 degrees.

<h3>Polygons</h3>

An octagon is a shape with 8 sides and 8 angles. The sum of an interior angle of an octagon is 1080 degrees.

<h3>Point of interseection</h3>

The point where the intersection of lines meets forms an angle of 45 degrees. Hence based on the given question, we can conclude that the measure of a single angle of deviation on a regular octagon is 45 degrees.

Learn more on polygons here: brainly.com/question/1487036

5 0
3 years ago
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Why can't the input value be negative?
ddd [48]

If you are working with time or days, you can't put in a negative value because if you are doing an experiment, you can't go back in time to do that experiment to gather data. (Time for the most part considered to be an input value so that's why I used it as an example.)

8 0
4 years ago
Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight o
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4 years ago
Write an equation for the line shown pictured in the graph.
guajiro [1.7K]

Answer:

<u>4y =  x + 13</u>

Step-by-step explanation:

The general equation of the line y = mx + c

where m is the slope and c is constant represent y-intercept

The line shown in the graph pass through the points (3,4) , (-1,3)

The slope of the line = (y₂-y₁)/(x₂-x₁) = (3-4)/(-1-3) = -1/-4 = 1/4

∴ y = (1/4) x + c

Substitute with the point (3,4) to find c

∴ 4 = (1/4) 3 + c

∴ c = 4 - 3/4 = 13/4

∴ y = (1/4) x + 13/4 ⇒ multiply both sides by 4

∴ 4y =  x + 13

So, The equation of the line in the graph: 4y =  x + 13

The equation can be written as <u>y = (1/4) x + 13/4  OR  4y - x = 13</u>

8 0
4 years ago
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ivanzaharov [21]

Answer:

<h2>a) Número de personas que suben a un autobús en una parada.</h2><h2>c) Conocer el ganador de la Liga de Campeones.</h2>

Step-by-step explanation:

This problem is about random experiments.

Random experiments are defined as experiments where the outcome can't be predicted. To ensure that result, the subjects are selected randomly. So, in this case, the right answer must be a situation where subjects are randomly present.

People taking the bus is a random experiment, because there's no the exact subjects in a bus at any time, it happens randomly.

Also, the winner of a sport league is also a random experiment, because it happens after several games which cannot be predicted.

Therefore, the right answers are a and c.

5 0
3 years ago
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