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Marat540 [252]
3 years ago
6

Noah built a fenced dog run that is 8 yards long and 6 yards wide. He placed posts at every corner and every yard along the leng

th and width of the run. How many posts did he use?
Mathematics
1 answer:
Karolina [17]3 years ago
6 0
There are 7 posts along one 8-yard side and 5 posts along one 6-yard side. It means that he used:

2 * 7 + 2 * 5 + 4 (posts on the corners) = 14 + 10 + 4 = 28 posts
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A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u
Kryger [21]

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

           g(x) = \frac{2x+1}{x}

A.)Consider

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

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

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

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

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

Also,

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

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

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

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

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


Since, f(g(x))=g(f(x))=x

Therefore, both functions are inverses of each other.


B.

For the Composition function f(g(x)) = f(\frac{2x+1}{x} )=x

Since, the function f(g(x)) is not defined for x=0.

Therefore, the domain is (-\infty,0)\cup(0,\infty)


For the Composition function g(f(x)) =g(\frac{1}{x-2} )=x

Since, the function g(f(x)) is not defined for x=2.

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8 0
4 years ago
Find the 100th term for the sequence. -9,-4, 1, 6, 11, .......
Paraphin [41]

Answer:

486

Step-by-step explanation:

for the 2nd term, add 5 to -9

for the 3rd, add 5 × 2 to -9

for the 4th, add 5 × 3 to -9

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for the 100th, add 5 × (100 - 1) to -9

=> 5 × 99 + (-9)

=> 486

8 0
3 years ago
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