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3 years ago

10

Use the graph to write the explicit rule of the arithmetic sequence.

1 answer:

Igoryamba3 years ago

6 0

Answer:

$f_n=7+\left(-2\right)\left(n-1\right)$

Therefore, option C is true.

Step-by-step explanation:

From the graph, we get the sequence

7, 5, 3, 1, ...

Here,

a₁ = 7 is the first element.

An arithmetic sequence has a constant difference 'd' and is defined by

$f_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$5-7=-2,\:\quad \:3-5=-2,\:\quad \:1-3=-2$

The difference between all the adjacent terms is the same and equal to

$d=-2$

substituting a₁ = 7 and d = -2 in the nth term of the sequence

$f_n=a_1+\left(n-1\right)d$

$f_n=7+\left(-2\right)\left(n-1\right)$

Therefore, option C is true.

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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 $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

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4 years ago

Gloria has 11 markers in a backpack. One of them is purple and one is gray. Find the probability Gloria will reach into the back

SCORPION-xisa [38]

Answer:

Step-by-step explanation:

She has 1 in 11 chances of getting the purple one

One of her choices is gone after she takes out the purple one. She has a 1 in 10 chance of taking out the gray one.

1/11 * 1/10 = 1/110

8 0

3 years ago

Monica [59]

The answer to this question is b

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3 years ago

Find a vector 3 units long in the opposite direction from v = 〈3, 1,-4).

lutik1710 [3]

Unit vector along the direction v = <3,1,-4> is :

$\hat{v} = \dfrac{3i + j -4k}{\sqrt{3^2 + 1^2 + 4^2}}\\\\\hat{v} = \dfrac{3i + j -4k}{5.1}$

So, unit vector opposing the $\hat{v}$ is :

$\hat{v'} = -\hat{v}\\\\\hat{v'} = -( \dfrac{3i + j -4k}{5.1})\\\\\hat{v'} = \dfrac{-3i - j +4k}{5.1}$

so, vector of magnitude 3 units in opposite direction from v is :

$\vec{V} = 3\hat{v'}\\\\\vec{V} = \dfrac{3}{5.1}( -3i -j+4k)$

Hence, this is the required solution.

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SVETLANKA909090 [29]

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3 years ago