Which notation indicates 2 congruent segments

After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives

[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]

Then taking differentials, you get

[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]

Replacing everything in the original integral then gives

[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]

Split up the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]

so that

[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]

5 students offers all the two subjects.

Student that offers Physic only = 15 students

Student that offers chemistry only  = 13 students

Students that offers only one subject = 28 students

Total student in the class = 35

20 offer physics.

18 offer chemistry

2 offer neither physics nor chemistry.

Therefore,

x = student that offer both subject

35 = 20 + 18 - x + 2

35 - 2 - 20 - 18 = -x

-5 = -x

x = 5

Therefore, 5 students offers all the two subjects.

Student that offers Physic only = 20 - 5 = 15

Student that offers chemistry only = 18 - 5 = 13

Students that offers only one subject = 13 + 15 = 28

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Answer:

7 > 24/4

Step-by-step explanation:

7 _ 24/4

Simplify 24/4

24/4 = 6

7 is greater than 6

7 > 24/4

7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.

Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:

1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.

2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.

3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.

The given numbers are:

7 and 24/4

To compare these numbers,

Convert the fraction 24/4 into the simplest form

Therefore,

[tex]\frac{24}{4} = 6[/tex]

Now since 7 is greater than 6 so we use ">" between them.

Hence,

The complete equation will be 7 > 24/4.

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Answer: 3 1/2

Step-by-step explanation:

"Of" is the same as multiplication so,

2/3 × 21/4=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

2 × 2/13 × 4 = 42/12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using

GCF(4/2 , 1/2) = 6

4/2 ÷ 6 1/2 ÷ 6 = 7/2

The fraction

7/2

is the same as

7÷2

Convert to a mixed number using

long division for 7 ÷ 2 = 3R1, so

7/2 = 3 1/2

Therefore:

2/3 of 21/4 = 3 1/2

Hopefully, I Helped

Answer:

0

Step-by-step explanation:

We are looking for the directional derivative of f at P in the direction of PQ.

First we compute

[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]

But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.

The answer is: 250 adult tickets were sold.

To be safe, prove that your answer is correct.

If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.

Explanation:

74 more than 250, or 250+74 is 324.

250+324=574.

Now, you know the answer is correct. It satisfies all of the given conditions.

Also, note that the difference between the number of student tickets and adult tickets is 74.

So, there are 250 adult tickets and 324 student tickets.

Answer:

$5

Step-by-step explanation:

Number of hours worked = 32

Total pay = $160

So, hourly rate

= Total pay/number of hours worked

= $160/32

= $5

Answer:

[tex] \frac{12 - 23 \sqrt{2} }{46} [/tex]

Step-by-step explanation:

you find the LCM

Answer: B. The mean is less than the median

Step-by-step explanation:

there are some that scored 51 which means - mean<median

Answer:

Part A. [tex]h=\frac{V}{\pi r^2}[/tex]

Part B. h= 4cm

Step-by-step explanation:

Answer:

3x - 6y - 74

Step-by-step explanation:

Given

3(5x - 2y) + 2(4x - 37) ← distribute parenthesis

= 15x - 6y + 8x - 74 ← collect like terms

= 23x - 6y - 74

Answer:

Distribute

3

(

5

−

2

)

+

2

(

4

−

3

7

)

{\color{#c92786}{3(5x-2y)}}+2(4x-37)

3(5x−2y)+2(4x−37)

1

5

−

6

+

2

(

4

−

3

7

)

{\color{#c92786}{15x-6y}}+2(4x-37)

15x−6y+2(4x−37)

2

Distribute

1

5

−

6

+

2

(

4

−

3

7

)

15x-6y+{\color{#c92786}{2(4x-37)}}

15x−6y+2(4x−37)

1

5

−

6

+

8

−

7

4

15x-6y+{\color{#c92786}{8x-74}}

15x−6y+8x−74

3

Combine like terms

1

5

−

6

+

8

−

7

4

15x−6y+8x−74

2

3

−

6

−

7

423x}}-6y-74

23x−6y−74

Solution

2

3

−

6

−

7

4

Step-by-step explanation:

Given:

Speed[tex]= \bold{9.2 \ \frac{miles}{hour}}[/tex]  

[tex]\therefore \\\\[/tex]

1-hour= 60 minutes

1-minutes=60 second

So

1-hour= 3600 second

Converting the given time into seconds:

Time= 6 minutes and 30 second

       [tex]=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\[/tex]

When 3600 seconds covers=9.2 miles

Then equation:

[tex]=\bold{\frac{9.2}{3600}}\\\\[/tex]

390 seconds covers:

[tex]=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\[/tex]  

Let

[tex]\bold{1 \ miles= 1760\ yard}\\\\[/tex]

Convert the traveling value into yards:

[tex]=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\[/tex]

Therefore, total traveling yards are"1754.072".  

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Speed of the person has been given as 9.2 miles per hour.

Therefore, speed of the person in miles per minute = [tex]\frac{9.2}{60}[/tex]

Duration for which the person is running = 6 minutes and 30 seconds

                                                                    = 6 minutes and [tex]\frac{30}{60}[/tex] minutes

                                                                    = 6.5 minutes

Since, Distance = Speed × Time

By substituting the values in the expression we can get the distance traveled.

Distance = [tex]\frac{9.2}{60}\times 6.5[/tex]

               = 0.9967 miles

Since, 1 mile = 1760 yards

Therefore, 0.99667 miles = 1760 × 0.99667

                                           = 1754.13 yards

Total distance traveled by the person is 1754.13 yards.

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Answer:

+or-6

Step-by-step explanation:

This is a trick question. The answer would be the first choice since you're multiplying -6 by +or-6, meaning that it could still end up as a negative or a positive.

Answer:

Step-by-step explanation:

Answer:

Solution given:

Equation of line is:

y=-⅔x

comparing above equation with

y=mx+c

we get

m=-⅔

So

Answer:

slope is -2/3

Step-by-step explanation:

I. It's linear equation

    y = mx + b

when y is output, x is input, m is slope and b is addition.

The statment above is y = -2/3x + 0

So -2/3 is slope or m.value

Hope that help :D

Answer:

5 in 12 chance or 42% probability of happening

4,3,2,1,0,-1, -2, -3, -4,

Equation of a line can be given by :

y = mx + b

Let's find the slope of the line (m) :

[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]

[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]

[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]

[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]

now let's solve for b :

[tex] \hookrightarrow \: y = mx + b[/tex]

Let's plug the values of x and y from the coordinates of a point .

[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]

[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]

[tex] \hookrightarrow \: b = - 1[/tex]

now, let's put the value of m (slope) and b (y-intercept) in the equation.

[tex] \hookrightarrow \: y = mx + b[/tex]

[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]

That's All, I hope it helped ya

Answer:

c) ten thousand dollars

Step-by-step explanation:

Answer:

2 one

Step-by-step explanation:

well if u go the other way for it to go right it is mf

Answer:

the point (9,-12) is also on the line

Step-by-step explanation:

by using the 2 points the equation is y=-4/3x

use x of 9

y = -12

it will also represent a direct variation function

so two of the 4 will be correct

Answer:

The point (9,-12) is also on the line

Step-by-step explanation:

Please give brainliest

Answer:

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

Step-by-step explanation:

Factor of [tex]x^{12}-1[/tex] is

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

Answer:

(x - y)²

Step-by-step explanation:

Given

(x + y)² - 4xy

= x² + 2xy + y² - 4xy

= x² - 2xy + y²

= (x - y)²

Answer:

[tex] {(x + y)}^{2} - 4xy = {x}^{2} + 2xy + {y}^{2} - 4xy \\ = {x}^{2} - 2xy + {y}^{2} \\ = {(x - y)}^{2} \\ thank \: you[/tex]

Answer:

125 p^3 g^3

Step-by-step explanation:

(5pg)^3

We know that (ab)^c = a^c * b^c

5^3 p^3 g^3

125 p^3 g^3

Yes, there is. It's 14. Hope this helps.

The relationship between the number of students that are good at a given subject is an illustration of sets.

We use the following representations:

[tex]M \to[/tex] Mathematics

[tex]E \to[/tex] English

[tex]P \to[/tex] Psychology

From the question, we have the following parameters

[tex]M = 45[/tex] -- Mathematics

[tex]M\ n\ E =15[/tex] -- Mathematics and English

[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology

[tex]E\ n\ P =16[/tex] -- English and Psychology

[tex]P=20[/tex] -- Psychology

[tex]All = 9[/tex] -- All 3 subjects

[tex]Total = 80[/tex] -- All students

The number of students that are good at mathematics only is as follows:

First, we calculate those that are good at mathematics and English only

[tex](M\ n\ E)' = M\ n\ E - All[/tex]

[tex](M\ n\ E)' = 15 - 9 = 6[/tex]

Then those that are good at mathematics and psychology only

[tex](M\ n\ P)' = M\ n\ P - All[/tex]

[tex](M\ n\ P)' = 13 - 9 = 4[/tex]

So, the students that are good at mathematics only are:

[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]

[tex]M' = 45 - 6 -4 -9[/tex]

[tex]M' = 26[/tex]

Hence, 26 students are good at Mathematics only.

To calculate the number of students that are not good in any of the subjects, we make use of the complement rule

[tex]A + A' = Total[/tex]

Where:

[tex]A \to[/tex] Students that are not good in any

[tex]A' \to[/tex] Students that are good in at least one

So, we have:

[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]

Where:

[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]

[tex](E\ n\ P) = 16-9 = 7[/tex]

The equation becomes:

[tex]A' =26 + 6 + 4+7+9[/tex]

[tex]A' =52[/tex]

Recall that:

[tex]A + A' = Total[/tex]

[tex]A = Total - A'[/tex]

[tex]A = 80 - 52[/tex]

[tex]A = 28[/tex]

Hence, 28 students are not good at all.

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Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

Step-by-step explanation:

LxB

8x7

equals :56

Area equals to 56cm

Answer:

[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]

Answer:

-22

Step-by-step explanation:

-18 + (-4) = -18 - 4 = -22

Answer:

scale factor = 3 : 11

Step-by-step explanation:

Given 2 similar figures with scale factor a : b , then

ratio of volumes = a³ : b³

Here

ratio of volumes = 27 : 1331 . so

scale factor = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11

Answer:

3:11

Step-by-step explanation:

Here, we are given that a room is painted by A, B and C so here three of them have done the work. So, we'll add all these fractions and assume the total work as 1 after that we will substract all the added ones from 1

Let us assume the room completely painted be 1

Now,

A has done 1/3, B has done 1/4 and C has done 1/5 work of the remaining

So, let us add them

Getting the L.C.M. The L.C.M of 3,4,5 is 60

Hence, 47/60 room has been painted

Remaining to paint

Total is assumed as 1

Work done = 47/60

Fraction of room needs to painted = 1 - 47/60

13/60 of the room needs to be painted, OPTION C IS CORRECT