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VashaNatasha [74]
3 years ago
7

For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distin

ct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1,000, what is the maximum possible sum of the length of x and the length of y?
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0

Answer:

16

Step-by-step explanation:

We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y < 1,000.

Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that

\large 2^n + 3*2^m < 1,000  

since \large 2^10 = 1,024 , then <em>n must be 9</em>. For n=9 we find the greatest integer m such that  

\large 2^9 + 3*2^m  

and<em> we find m=7 </em>

 and  \large x=2^9 , \large y=2^7  are the numbers we are looking for and the sum of their length is 9+7 = 16.

So, 16 is the maximum possible sum of the length of x and the length of y.

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the factors of 12 are: 1,2,3,4,6,12 
the factors of 21 are: 1,3,7,21 

1 and 3 are both common factors of 12 and 21.</span>
7 0
3 years ago
Given a line with slope m = -3/2 and a point (5, -6), what's the y-coordinate of the y- intercept?​
Svetlanka [38]

Answer:

3/2

Step-by-step explanation:

y = mx + b

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2 years ago
In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio o
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Answer:

1/14:5/7:3/14

Step-by-step explanation:

Since orange=15

Apple=5

Coconut milk=50

50+15+5

70

So

Orange=15/70

Divide both by 5

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Apple=5/70

Divide both by 5

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Coconut milk=50/70

Divide both by 10

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So the ratio of apple to coconut to orange

1/14:5/7:3/14

8 0
3 years ago
Let x and y be inversely related. if x is 5 when y is 6, find y when x is 3​
VLD [36.1K]

Answer:

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Step-by-step explanation:

5 0
2 years ago
Given the trinomial, what is the value of the coefficient B in the factored form?
Ivenika [448]

Answer:

B = 6

Step-by-step explanation:

2x^2 + 4xy − 48y^2

Factor out 2

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What 2 numbers multiply to -24 and add to 2

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2 ( x+6y)( x-4y)

8 0
3 years ago
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