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PolarNik [594]
3 years ago
15

Alex's dog weighs 7 times as much as her cat. Together, the two pets weigh 72 pounds. How much does Alex's dog weigh?

Mathematics
1 answer:
raketka [301]3 years ago
7 0
D=dog's weight
c=cat's weight
d=7c
d+c=72
sub 7c for d
7c+c=72
8c=72
divide both sides by 8
c=9
d=7c
d=7(9)
d=63
dog=63lb
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b)

f(g(x))=f(\sqrt{x}-2)=(\sqrt{x}-2)^2-x=\sqrt{x}^2-2*2*\sqrt{x}+2^2-x=-4\sqrt{x}+4

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c)

f(g(x))=f(\frac{1}{x-1})=(\frac{1}{x-1})^2=\frac{1}{(x-1)^2}

g(f(x))=g(x^2)=\frac{1}{x^2-1}

The domain of f(g(x)) is the set of reals except the 1 and the domain of g(f(x)) is the set of reals except the 1 and -1

d)

f(g(x))=f(\frac{1}{x-1})=\frac{1}{(\frac{1}{x-1}-1)}=\frac{1}{\frac{2-x}{x-1}}=\frac{x-1}{2-x}

g(f(x))=g(\frac{1}{x+2})=\frac{1}{(\frac{1}{x+2}-1)}=\frac{1}{\frac{-x-1}{x+2}}=\frac{x+2}{-x-1}

The domain of f(g(x)) is the set of reals except 2, and the domain of g(f(x)) is the set of reals except -1.

e)

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The domain of f(g(x)) is the set of nonnegative reals except -3. The domain of g(f(x)) is the set of nonnegative reals except -2.

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