I can only give possible combination of the ages. Had the sum of the ages been given, then the 3 specific numbers would have been derived.
We need to do prime factorization of 72.
72 ÷ 2 = 36
36 ÷ 2= 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 1 = 1
1 x 2 x 2 x 2 x 3 x 3 = 72
Possible combinations:
1 x 8 x 9 = 72 1 + 8 + 9 = 18
1 x 4 x 18 = 72 1 + 4 + 18 = 23
2 x 4 x 9 = 72 2 + 4 + 9 = 15
3 x 4 x 6 = 72 3 + 4 + 6 = 13
Answer:
5n + 10d represented the money spend by the Amy in playing board games of cost $5 and $10 .
Step-by-step explanation:
As given
Amy and Mary are playing a board game that uses game money if $5 and $10.
At the end of the game, Amy has n bills worth $5 each and d bills worth $10 each .
Total amount of n bills = 5n
Total amount of d bills = 10d
Thus
Total money spend by the Amy in playing board games = Total amount of n bills + Total amount of d bills
= 5n + 10d
Therefore 5n + 10d represented the money spend by the Amy in playing board games of cost $5 and $10 .
Answer:
<h2>One solution.</h2>
Step-by-step explanation:
The given question is
<em>Does the following system have One Solution, No Solution, or Infinite Solutions.
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To solve this system, we just need to multiply the first equation by -1, and then sum those equations.
![-y = -4x - 8\\y = -5x + 3](https://tex.z-dn.net/?f=-y%20%3D%20-4x%20-%208%5C%5Cy%20%3D%20-5x%20%2B%203)
![0=-9x-5\\5=-9x\\x=-\frac{5}{9}](https://tex.z-dn.net/?f=0%3D-9x-5%5C%5C5%3D-9x%5C%5Cx%3D-%5Cfrac%7B5%7D%7B9%7D)
Then, we use this value to find the other one
![y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}](https://tex.z-dn.net/?f=y%3D4x%2B8%5C%5Cy%3D4%28-%5Cfrac%7B5%7D%7B9%7D%20%29%2B8%5C%5Cy%3D-%5Cfrac%7B20%7D%7B9%7D%2B8%5C%5Cy%20%3D%5Cfrac%7B-20%2B72%7D%7B9%7D%20%5C%5Cy%3D%5Cfrac%7B52%7D%7B9%7D)
As you can observe, the system of equations have a unique solution.
Therefore, the answer is one solution.
For this case we have the following polynomial:
![60x ^ 2 + 48x + 24](https://tex.z-dn.net/?f=%2060x%20%5E%202%20%2B%2048x%20%2B%2024%20)
What we must do for this case is to factor the polynomial, so that we have:
1) The number of bottles
2) the weight of each bottle.
We have then:
![12 (5x ^ 2 + 4x + 2)](https://tex.z-dn.net/?f=%2012%20%285x%20%5E%202%20%2B%204x%20%2B%202%29%20)
Answer:
A factorization that could represent the number of water bottles and weight of each water bottle is:
![12 (5x ^ 2 + 4x + 2)](https://tex.z-dn.net/?f=%2012%20%285x%20%5E%202%20%2B%204x%20%2B%202%29%20)