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2 years ago

Please help with this

Mathematics

2 answers:

Dmitriy789 [7]2 years ago

8 0

Step-by-step explanation:

All has been answered... send me any questions at comments

igor_vitrenko [27]2 years ago

3 0

27,30,23,92,20,22 and yea that’s the answe

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EDITED QUESTION ... answer it >:]

sammy [17]

Answer:

Step-by-step explanation:

because the line has to run through the origin, so that is non-proportional.

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3 years ago

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Talja [164]

Answer:

y = -3x

Step-by-step explanation:

Given the illustration of the graph, we can see that the line is going downhill. This would indicate that the slope is negative, so the choices would be narrowed down y = -3x or y = -x. Looking at the line, we can use two points to find the difference in 'y' over the difference in 'x', or slope. Using the origin (0,0) as one point, we can go down 3 and over 1 to get to the second point of (1, -3). This would be an overall change of -3, giving us the final answer of:

y = -3x

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3 years ago

Find a and b such that gcd(a, b) = 14, a > 2000, b > 2000, and the only prime divisors of a and b are 2 and 7.

choli [55]

Answer:

$a = 2^\alpha.14 \ ,\alpha\geq 8\\b = 7^\delta.14 \ , \delta\geq 3$

Step-by-step explanation:

As 2 and 7 are the only prime divisors of both $a$ and $b$ we know that both can be written as:

$a = 2^\alpha . 7^\beta \ , \alpha ,\beta\ \in \mathbb{N}_{0}\\b = 2^\gamma . 7^\delta \ , \gamma ,\delta\ \in \mathbb{N}_{0}\\$

Where $\mathbb{N}_{0}$ is the set of all natural numbers adding the zero (careful because this part is important as I'll explain next).

We also know that 14 divides both numbers and that is actually the greatest common divisor between them. So we can rewrite a and b as follows:

$a = 2^\alpha . 7^\beta.14 \ , \alpha ,\beta\ \in \mathbb{N}_{0}\\b = 2^\gamma . 7^\delta.14 \ , \gamma ,\delta\ \in \mathbb{N}_{0}\\$

Why do I write them like this? Because this way is easier to observe that if $\alpha$ and $\gamma$ were both greater than zero, then 28 would divide both hence 14 wouldn't be their g.c.d.. Likewise, if $\beta$ and $\delta$ were both greater than zero, then 98 would divide both and once again, 14 wouldn't be their g.c.d.

So either of them has to be equal to zero. And then we have that

$a = 2^\alpha.14 \\b = 7^\delta.14$

All we have left to do is find the possible values for $\alpha$ and $\delta$ so that $a>2000 \ , b>2000$ and that only happens if $\alpha\geq 8$ and $\delta\geq 3$