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3 years ago

What is the GCF of 36 and 84? 4 6 12 18

Mathematics

2 answers:

Vadim26 [7]3 years ago

7 0

The greatest common factor is 12 because 12 times 3 is 36 and 12 times 7 is 84.

Hope this helps! :)

zepelin [54]3 years ago

5 0

To get the GCF of 36 and 84 we need to factor each value first and then we have to choose all the copies of factors and multiply them:

36: 2233
84: 223 7
_________
GCF = 223

The Greates Common Factor (GCF) is: 2 x 2 x 3 = 12

Answer: 12

Hope this helps you! :)

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$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

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Then translating 1 unit down:

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As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

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