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V125BC [204]
3 years ago
10

GCF of 4x^2y^2, 3xy^4, and 2xy^2

Mathematics
1 answer:
allsm [11]3 years ago
5 0
The greatest common factor would be xy^2 because these are the only factors that they all have in common. The second term only has 1 x, so only 1 x is part of the gcf.

The 1st and 3rd terms each have y^2 therefore making it part of the gcf as well.
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The sum of the digits of a two-digit number is 5. If the number is multiplied by 3, the result is 42. Write and solve a system o
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A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit

"The sum of the digits is 5"
x + y = 5

The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]

The number is: 10x + y
3(10x + y) = 42

The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42

Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out

-3x - 3y = -15
30x + 3y = 42
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27x + 0 = 27
x = 1

then plug x = 1 into either equation to find y

1 + y = 5
y = 4

remember the x and y represent digits so the number xy is 14
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