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2 years ago

Which of the following pairs of functions are inverse’s of each other?

Mathematics

1 answer:

liubo4ka [24]2 years ago

5 0

The answers in C are inverses of each other.

In order to find the inverse of any equation, you simply switch the x and f(x) values and then solve for the new f(x). What it will result in is your new inverse function. If we do this for each of the problems above, only one will produce the second equation properly. See the work below for how to do it for C.

f(x) = 11x - 4 ---> Switch the x and f(x)

x = 11f(x) - 4 ----> Add 4 to both sides

x + 4 = 11f(x) ----> Divide both side by 11

$\frac{x+4}{11}$ = f(x) ----> Now put in the correct order

f(x) = $\frac{x+4}{11}$

Since our inverse matches the g(x) function, this means that C is the correct answer.

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If 2.5 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumfe

Natalka [10]

Answer:

They encircle the planet $3.76\times 10^{11}$ times.

Step-by-step explanation:

Consider the provided information.

We have 2.5 mole of dust particles and the Avogadro's number is $6.022\times 10^{23}$

Thus, the number of dust particles is:

$2.5\times 6.022\times 10^{23}=15.055\times 10^{23}$

Diameter of a dust particles is 10μm and the circumference of earth is 40,076 km.

Convert the measurement in meters.

Diameter: $10\mu m\times \frac{10^{-6}m}{\mu m} =10^{-5}m$

If we line up the particles the distance they could cover is:

$15.055\times 10^{23}\times 10^{-5}=15.055\times 10^{18}=1.5055\times 10^{19}$

Circumference in meters:

$40,076km\times \frac{1000m}{1km}=40,076,000 m$

Therefore,

$\frac{1.5055\times 10^{19}}{40,076,000} = 3.76\times 10^{11}$

Hence, they encircle the planet $3.76\times 10^{11}$ times.

8 0

2 years ago

He makes $316 a week and $23 for every sale he makes. He has to pay his rent this week that is $500, so he will need to make at

Lyrx [107]

let x be the number of sales Hayward needs to make

316+23x > or equals to 500

23x> or equals to 184

x> or equals to 8

4 0

2 years ago

The sum of the arithmetic progression 4, ..., 76 is 1920. Find the number of terms and the common difference.

valkas [14]

<u>Number of terms = 48</u>

<u>common difference = 1.5</u>

This question involves the concept of Arithmetic Progression.

The formula for sum of an arithmetic progression series with first and last term given is;

$S_{n}$ = $\frac{n}{2}$ (a + l)

where;

a = first term

l = last term

n = number of terms

From the given sequence, we see that;

first term; a = 4

last term; l = 76

Sum of A.P; $S_{n}$ = 1920

Plugging in relevant values into the sum of an AP formula, we have;

1920 = $\frac{n}{2}$ (4 + 76)

simplifying this gives;

1920 = 40n

n = 1920/40

n = 48

Formula for nth term of an AP is;

$t_{n}$ = $a_{1}$ + (n - 1)d

where;

$a_{1}$ is first term

d is common difference

n is number of term

$t_{n}$ is the nth term in question

the 48th term is 76

Thus;

76 = 4 + (48 - 1)d

76 - 4 = 47d

72 = 47d

d = 72/47

d ≈ 1.5

Thus;

Number of terms = 48

common difference = 1.5

Read more at; brainly.com/question/16935540

4 0

2 years ago

What is the volume of a prism which has a base of 5 m by 3m, and a height of 4m?

wlad13 [49]

If you multiplied the base times the width times the height you would get a final answer of 60m.

4 0

2 years ago

Write an equation for the description.A number x increased by 13 is 116

seropon [69]

Answer:

X+13=116

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers