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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?

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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3 years ago

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

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

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

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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.

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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

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3 years ago