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Illusion [34]
3 years ago
15

What is the greatest common factor of the following monomials: 12g^5h^4 g^5h^2

Mathematics
1 answer:
muminat3 years ago
6 0

Answer:

g^5h^2

Step-by-step explanation:

12g^5h^4, g^5h^2

This is one way of doing it. Break down every number and every variable into a product of the simplest factors. Then see how many of each factor appear in both monomials.

12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h

g^5h^2 = g * g * g * g * g * h * h

So far you see every single prime factor of each monomial.

Now I will mark the ones that are present in both. Those are the common factors.

12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h

g^5h^2 = g * g * g * g * g * h * h

The greatest common factor is the product of all the factors that appear in both monomials.

GCF = g * g * g * g * g * h * h = g^5h^2

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A concert sold general admission tickets for $47.50 and lower-level seating for $97.50. The 995 tickets sold took in $68,762.50.
BabaBlast [244]

Answer: 565 general admission and 430 lower-level seating tickets sold (Answer (D))

Steps:

Let x be the number of general admission tickets, and y be the number of lower level tickets.

Set up the two equations:

68762.5 = x * 47.50 + y * 97.50       (total price as a sum of individual volumes)

x + y = 995    (sum of individual count = total count of tickets sold)

solve for x, y:

x = 995 - y

plug into the first equation:

68762.5 = (995-y) * 47.50 + y * 97.50

solve for y:

y = 430

then x = 565

x = 565 and y = 430


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