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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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25x10^6 how do you do this question??
Mazyrski [523]

Answer:

25,000,000x

Step-by-step explanation:

10^6=1,000,000

25*1,000,000x

Mulitipli the numbers: 25 * 1,000,000 = 25,000,000x

7 0
3 years ago
Read 2 more answers
P is located at (8,-7) and Q is located at (-6,-3) on the coordinate plane
Readme [11.4K]

Answer:

Step-by-step explanation:

1,-5

5 0
2 years ago
Eight year-old Alex is learning to ride a
cestrela7 [59]

Answer:

The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.

Therefore, the age of the horse, in human years, when Alex was born was 42 years.

Step-by-step explanation:

Current age of Alex = 8

Current age of the horse in human years = 50

Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.

Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:

The age of the horse, in human years, when Alex was born = 50 - 8 = 42

Therefore, the age of the horse, in human years, when Alex was born was 42 years.

This can be presented in a table as follows:

                               Age of Alex        Age of the Horse (in human years)

Eight years ago              0                                           42

Current age                    8                                           50

6 0
3 years ago
The value of y varies directly with x and y = 4.5 when x = 0.5. find y when x = 10
Pepsi [2]
So what you asked this is what I got

x(y) = 4.5

If x= 0.5 then 

0.5(y) = 4.5
y=9

x(y) = 4.5

10(y) = 4.5
y= 0.45



hope this helps :)





3 0
3 years ago
Which of the following statements describes one part of completing the square for x 2 + 4x = 32?
Westkost [7]

SOS:

Answer:

Take the square root of 36 and subtract 2.

Step-by-step explanation:

x^2+4x=32\\(\frac{1}{2}*4=2; 2^2=4) : x^2+4x+4=36\\\sqrt{(x+2)^2}=\sqrt{36}\\ x+2=±6: -2+6=4, -2-6=-8

<em>Hope this helps!!</em>

7 0
3 years ago
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