8.) Simplify each expression:
a.) 2x + 4x + 8x
b.) 5(x + 2) + 3x
c.) 6(2x + 1) - 5x + 7

[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to 0}}\dfrac{sinx-sin3x}{sins3x-sinx}[/tex]

[tex]\boxed{\sf \displaystyle\lim_{x\to 0}\dfrac{f(x)}{g(x)}=\dfrac{\lim_{x\to 0}f(x)}{\lim_{x\to 0}g(x)}}[/tex]

Now

[tex]\\ \sf\longmapsto \displaystyle{\dfrac{\lim_{x\to 0}sinx-\lim_{x\to 0}sin3x}{\lim_{x\to 0}sin3x-\lim_{x\to 0}sinx}}[/tex]

[tex]\boxed{\sf \displaystyle{\lim_{x\to 0}}f(x)=f(a)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin0-sin3(0)}{sin3(0)-sin0}[/tex]

[tex]\\ \sf\longmapsto \dfrac{0-0}{0-0}[/tex]

[tex]\\ \sf\longmapsto \dfrac{0}{0}[/tex]

[tex]\\ \sf\longmapsto 0[/tex]

Step-by-step explanation:

Using the following property of logarithms,

[tex]\ln{\left(\dfrac{a}{b}\right)} = \ln{a} - \ln{b}[/tex]

we can write the given equation as

[tex]\ln{(x^2 + 1)} - \ln{(x^2 - 1)} = \ln{\left(\dfrac{x^2 + 1}{x^2 - 1}\right)}[/tex]

[tex]\:\:\:\:\:\:\:\:\:= \ln{\dfrac{x(x + 1)}{x(x - 1)}} = \ln{\left(\dfrac{x + 1}{x - 1}\right)}[/tex]

But recall that [tex]\ln{e} = 1[/tex] so we can write our original equation as

[tex]\ln{\left(\dfrac{x + 1}{x - 1}\right)} = \ln{e}[/tex]

or simply

[tex]\dfrac{x + 1}{x - 1} = e[/tex]

Multiplying both sides by [tex](x - 1),[/tex] we get

[tex]x + 1 = e(x - 1)[/tex]

Solving for x, we get

[tex]x = \dfrac{e + 1}{e - 1}[/tex]

Answer:

a) { 15, 16, 17, 18, 19, 20}

b) { 4, 8, 12, 16, 20}

Answer:

4

Step-by-step explanation:

h=8

p=4√3

b=?

By using Pythagoras theorem,

b=√h²-p²

=√8²-(4√3)²

=√64-48

=√16

=4

To find out the unit vector in the same direction of other vector, we can calculate the magnitude of its vector and then divide all coordinates by the magnitude, remember that the definition of a unit vector is that its magnitude is 1.

We can calculate the magnitude of a 2D vector as

                                              [tex]\Large\displaystyle\text{$\begin{gathered}v = \left(x, y\right)\\ \\\|v\| = \sqrt{x^2 + y^2}\end{gathered}$}[/tex]

I'll call the vector (-4, 7) as v, so the magnitude of v is

                                       [tex]\Large\displaystyle\text{$\begin{gathered}v = \left(-4, 7\right)\\ \\\|v\| = \sqrt{\left(-4\right)^2 + \left(7\right)^2}\\ \\\|v\| = \sqrt{65}\\ \\\end{gathered}$}[/tex]

So the unit vector that i'll call as v with an hat is

                                                   [tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\end{gathered}$}[/tex]

The vector divided by its magnitude, when we divide a vector by a scalar it's the same as divide all the coordinates, so

                                      [tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\\ \\\hat{v} = \frac{v}{\sqrt{65}}\\ \\\hat{v} = \frac{\left(-4, 7\right)}{\sqrt{65}}\\ \\ \boxed{\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)}\end{gathered}$}[/tex]

We can also remove the square root from the denominator, then

                            [tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}, \frac{7}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4\sqrt{65}}{65}, \frac{7\sqrt{65}}{65}\right)\\ \\\end{gathered}$}[/tex]

Use what you prefer!

Hope you liked it

Questions? Ask me in the comments

Answer:

(3-2)-8+7 is the answer do fast fast

Since log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b) for any logarithm base, we have

[tex]\dfrac{\log_x(64) + \log_x(4) - \log_x(8)}{\log_x(1024)} = \dfrac{\log_x\left(\dfrac{64\times4}8\right)}{\log_x(1024)} = \dfrac{\log_x(32)}{\log_x(1024)}[/tex]

Then using the change-of-base identity, we have

[tex]\dfrac{\log_x(32)}{\log_x(1024)} = \log_{1024}(32)[/tex]

But we also know that 2¹⁰ = 1024 and 2⁵ = 32, so we can back up slightly and instead write

[tex]\dfrac{\log_x(32)}{\log_x(1024)} = \dfrac{\log_x(2^5)}{\log_x(2^{10})} = \dfrac{5\log_x(2)}{10\log_x(2)}[/tex]

Then the logarithms cancel and you're left with 5/10 = 1/2.

Answer:

19 cm

Step-by-step explanation:

I believed the answer is 19 cm because

AC = 7cm

CB= 12cm

AB= AC+CB

AB= AC+CBAB=7cm+12cm

AB=19cm

I hope this helps, dont hesitate to ask for any question.

.Mark me as brainliest is appreciated.Tq!!

Answer:

0.2

Divide 12 by 60

Answer:

Step-by-step explanation:

Answer:

44 cookies

Step-by-step explanation:

add the remaining cookies to the ones he gave away

(8+14)=22

double that

22x2

answer

44

Answer:

always

Step-by-step explanation:

They would always be equivalent if the left side equals the right side no matter what value you place into the variable

Two functions are always equivalent if they produce the same output for a specific input value. always, sometimes, or never.

Given that,
A statement is given, we have to fill the black statement is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Let two function, f(x) , g(x),
at x = a
both functions give the same value, then the two functions are equivalent. So,t wo function are always equivalent if they produce the same output for a specific input value. always, sometimes, or never.

Thus, two functions are always equivalent if they produce the same output for a specific input value. always, sometimes, or never.

learn more about function here:

brainly.com/question/21145944

#SPJ2

Answer:

32%-39% Is the correct answer

Exact Answer :-

[tex]35.24[/tex]%

Answer:-

[tex]\\ \longmapsto[/tex]32%-39%

[tex]hopes\:its\:helps\:you[/tex]

P = 2W + 2L

2W = P - 2L

W = (P - 2L)/2

Answer:

35.

Step-by-step explanation:

a^2 + b^2 = (a + b)^2 - 2ab

Substituting the given values:

25 = (a + b)^2 - 2*5

(a + b)^2 = 25 + 10

(a + b)^2 = 35

Answer:

17 67899887753 o

haggis to get a chance to get a chance

up to you and I don't know how I turned

him to be read by signs or something like that but

Step-by-step explanation:

join us for a while ago and I don't know

Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer.....

Hope it helps!

Brainliest pls!

Follow me! :)

Answer:

141

Step-by-step explanation:

52/4+8(4)^2

13+128=141

Answer:

141

Step-by-step explanation:

a/4  + 8b^2

Let a =52  and b =4

52/4  + 8(4)^2

Exponents first

52/4 + 8(16)

Multiply and divide

13+128

Add

141

Answer:

1.6%

Step-by-step explanation:

2376/2338= 1.016

1.016-1 = .016 * 100

1.6%

hope it helps :)

The percent difference is 1.6% Eris larger than Pluto.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that

The diameter of Eris is 2,338 km and

The diameter of Pluto is 2376.6 km

So the ratio of diameter = 2376/2338 = 1.016

The percent difference = (1.016 - 1)×100

The percent difference = 0.016 × 100

The percent difference = 1.6%

Hence, the percent difference is 1.6% Eris larger than Pluto.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Answer:

your smart enough

Step-by-step explanation:

Answer:

please provide the question so i can help :)

Step-by-step explanation:

Answer:

raymon hit the ball 60% of the time sorry not to sure about the question please expand

Step-by-step explanation:

Answer:

x=8,10if this helps then your welcome if not I apologize

9514 1404 393

Answer:

  285

Step-by-step explanation:

Put the numbers where the variables are and do the arithmetic.

  [tex]\dfrac{x^2y-2z}{4}=\dfrac{12^2\cdot8-2\cdot6}{4}=\dfrac{144\cdot8-2\cdot6}{4}\\\\=\dfrac{1152-12}{4}=\dfrac{1140}{4}=\boxed{285}[/tex]

Answer:

Step-by-step explanation:

[tex]8p^2-2p+15 + (11-2p^2-1)\\=(8p^2-2p^2)-2p +(15+11-1)\\=6p^2 -2p +25[/tex]

Answer:

190.548

Explanation:

1st grader maths

Answer:

190.548

Step-by-step explanation:

Literally add everything together

Answer:

10%

Step-by-step explanation:

50+50=100

45+45=90

100-90=10

Answer:

49 × 3.14 = 153.86

Step-by-step explanation:

1/3 × 3.14 × 49 × 3 = 153.86

Step-by-step explanation:

option B is correct answer

Answer:

Part 1 is B and Part 2 is A

Step-by-step explanation:

Edg 2021