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4vir4ik [10]
2 years ago
12

City code says you need to have at least 50 toilet stalls, but each bathroom can only have 10 stalls. You need to have the same

number of bathroom stalls as bathrooms for men and women. How many bathrooms (with 10 stalls each) must you built?
Mathematics
1 answer:
Vlada [557]2 years ago
3 0

Answer:

2 bathrooms (with 10 stalls each) for men and 2 bathrooms (with 10 stalls each) for women. (4 bathrooms in all)

Step-by-step explanation:

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factor the polynomial completely and SHOW WORK i’ve been on it for the past 30 minutes and I want to cry 24x^3-78x^2+45x NO LINK
Svetllana [295]

9514 1404 393

Answer:

  3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

  (3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

  120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

  121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

  8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

  =  (8x^2 -20x) +(-6x +15)

  = 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

  = (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

  24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)

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