How did the first line get to the second line??? (Check Picture)

Looks like the integral is

[tex]I=\displaystyle\int (4x-6)(x^2-3x+1)^5\,\mathrm dx[/tex]

If you we substitute [tex]y=x^2-3x+1[/tex] and [tex]\mathrm dy=(2x-3)\,\mathrm dx[/tex], we get

[tex]I=\displaystyle2\int(2x-3)(x^2-3x+1)^5\,\mathrm dx=2\int y^5\,\mathrm dy[/tex]

Now use the power rule, and replace y accordingly:

[tex]I=\dfrac{2y^6}6+C=\dfrac{y^6}3+C=\boxed{\dfrac{(x^2-3x+1)^5}3+C}[/tex]

Answer:

The average rate of function of f on the given interval is -1.

Step-by-step explanation:

Recall that the average rate of change is simply the slope of the function between two points.

We are given the function:

[tex]f(x)=x^2-4[/tex]

And we want to find its average rate of change on the interval [-4, 3].

Evaluate the two endpoints:

[tex]\displaystyle \begin{aligned} f(-4) & = (-4)^2 - 4 \\ \\ & = 16 - 4 \\ \\ & = 12\end{aligned}[/tex]

Likewise:
[tex]\displaystyle \begin{aligned} f(3) & = (3)^2 - 4 \\ \\ & = 9 - 4 \\ \\ & = 5\end{aligned}[/tex]

Recall that slope is given by:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x}[/tex]

Hence, the average rate of change is:
[tex]\displaystyle\begin{aligned} \text{Avg Rate of Change} & = \frac{(5)-(12)}{(3)-(-4)} \\ \\ &= \frac{-7}{7} \\ \\ & = -1\end{aligned}[/tex]

In conclusion, the average rate of function of the given function on the given interval is -

Answer:

n = 2

Step-by-step explanation:

- 6n - 2n = 16

- 8n = 16

n = 16/-8

n = -2

Answer:

[tex] - 6n \: - 2n \: = 16[/tex]

[tex] = ) - 8n \: = 16[/tex]

[tex] = )n \: = \frac{16}{ - 8} [/tex]

[tex] = )n \: = - 2[/tex]

Answer:

274.556 degrees to the nearest thousandth.

Step-by-step explanation:

33 ' = 33/60 = 0.55 degrees.

23" = 23/60 minutes

= 23/60 / 60 = 0.00639 degrees

So the answer is 274 + 0.55 + 0.00639 degrees

=

274.55639 degrees.

he got 0.08 percent questions correct

Answer:

72%

Step-by-step explanation:

A percentage is a number out of 100.  For example, 32/100 is 32%.  What you want to do with percentages is multiply the denominator of a fraction so it becomes 100 and multiply that same number to the numerator.  Sort of like a ratio!

If Mark got 18/25, we can multiply 25 by 4 to get 100 as the denominator.

Since you multiplied the denominator by 4, you have to multiply the numerator by 4 as well.  

18 times 4= 72.  So the numerator is 72 and the denominator is 100.  The fraction is 72/100, which is 72% since it is out of 100.

Answer:

D. The oldest is 92 youngest 49

Step-by-step explanation:

we can get the answer by pairing each of the values on the left hand side that is these values 4 5 6 7  9 with values on the right.

the first age from the top row is 49 the second is 49

from the second row it is 50 50 51 51 52 5 59

from the 3rd row 61 62 63 64 64 65 6

from the forth row t s 71 72 73 73 74 75 7

from the fifth row it is 80 81 83 87

from the sxth row it is 91 92.

each of the numbers  have just written out represents age. the oldest age there is 92 whle the youngest s 49. It is simply each number under attorney paired wth stem to make a number.

I added an attachment with the pairing

Answer:

170.097

Step-by-step explanation:

1 ounce = 28.3495 grams.

28.3495 x 6 = 170.097

Answer:

170.097 grams            Mark me as brainliest!!!!

Step-by-step explanation:

Answer:

4:5

Step-by-step explanation:

Davina received 50 votes

Binh reveived 40 votes

It asked for ratio of Binh’s votes to Davina’s

so the ratio is first Binh's 40 to Davina's 50     that's 40 to 50

It want it in simplest form so you find the greatest common factor of 40 and 50 which is 10.

40/10 and 50/10 is 4 to 5

So the answer is 4:5(The ":"  means  "to")

The ratio of Binh’s votes to Davina’s votes is 4:5

The comparison of two numbers or quantities by division is known as the ratio.

Given that, In the student council election, Davina received 50 votes, Binh received 40 votes and Eden received 80 votes.

Required ratio = Binh’s votes \ Davina’s votes  

= 40/50

= 4/5

Hence, The ratio of Binh’s votes to Davina’s votes is 4:5

For more references on ratios, click;

https://brainly.com/question/13419413

#SPJ3

Step-by-step explanation:

To find the distance between two points, we have to use the distance formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

Let's solve for line PQ first. We plug in the points into the formula and solve from there.

P: (-5, 1)

Q: (-2, -5)

[tex]PQ=\sqrt{(-2+5)^2+(-5-1)^2 }[/tex]

[tex]PQ=\sqrt{(3)^2+(-6)^2 }[/tex]

[tex]PQ=\sqrt{9+36}[/tex]

[tex]PQ=\sqrt{45}[/tex]

[tex]PQ=3\sqrt{5}[/tex]

Now, let's solve line ML.

M: (5, 3)

L: (2, -3)

[tex]ML=\sqrt{(2-5)^2+(-3-3)^2 }[/tex]

[tex]ML=\sqrt{(-3)^2+(-6)^2}[/tex]

[tex]ML=\sqrt{9+36}[/tex]

[tex]ML=\sqrt{45}[/tex]

[tex]ML=3\sqrt{5}[/tex]

Answer: 3√5, 3√5, yes, they are congruent.

Answer:

[tex] {4}^{x - 1} = \frac{49}{4} [/tex]

Step-by-step explanation:

My work is in the attachment but I essentially used a hefty bit of Algebraic manipulation to turn 2^x into 4^(x-1) and then isolating that bit.

Comment if you have any questions.

Answer:

49/4

Step-by-step explanation:

4^x-1 = (2^x)^2/4 = 7^2/4 = 49/4

Answer:

256x^8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the differential equation dy/dx = 5y/x subject to the condition y = 4 and x = 1. Using the variable separable method of solving differential equation, we will have;

dy/dx = 5y/x

Separate the variables

dy/5y = dx/x

Integrate both sides of the expression

[tex]\frac{1}{5}\int\limits \frac{1}{y} \, dy = \int\limits \frac{dx}{x} \\ \\\frac{1}{5}lny = lnx + C\\\\lny = 5lnx+5C\\[/tex]

using the initial condition y = 4 while x = 1

ln4 = 5ln1 + 5C

ln4 = 0+5C

C = ln4/5

Substituting the value of C back into the expression;

[tex]lny = 5 lnx+5(ln4/5)\\lny = 5lnx+ln4\\lny = lnx^5+ln4\\lny = ln(4x^5)\\y = 4x^5[/tex]

Hence the solution to the differential equation is y = 4x⁵

b) Given 4(du/dt) = u²

du/dt = u²/4

du/ u² = dt/4

u⁻²du = 1/4 dt

integrate both sides of the equation

[tex]\int\limit {u^{-2}} \, du = \int\limits\frac{1}{4} \, dt\\\\\frac{u^{-1}}{-1} = \frac{t}{4} + C\\\\\frac{-1}{u} = \frac{t}{4} + C[/tex]

Imputing the initial condition u(0) = 7 i.e when t = 0, u = 7

[tex]\frac{-1}{7} = \frac{0}{4} + C\\\\\frac{-1}{7} = C\\[/tex]

[tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]

Hence the solution to the DE is [tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]

I'm not sure what you're really talking about.

But I think you are talking about fractions.

In fractions there are two places

The number that goes on the top is numerator.

Answer:

2000 kilograms

Step-by-step explanation:

Answer:

Tyler had 7/12  pound of trail mix

He ate 4/12 of it i.e

7/12-4/12=7-4/12

3/12=1/4

He has 1/4 of trial mix left

Answer:

0.137.

Step-by-step explanation:

Given that

Sample size = 1100

Afraid to fly = 10 %

Mean = n x p

Mean = 1100 x 0.1 = 110

Variance = n p q

Variance = 1100 x 0.1 x 0.9 = 99

Standard deviation = [tex]\sqrt{n\times p\times q}[/tex]

S.D.=[tex]\sqrt{1100\times 0.1\times 0.9}[/tex]

S.D.=9.94

By using Normal distribution

[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]

[tex]Z=\dfrac{121-110}{9.94}[/tex]

Z=1.16

[tex]P(X>121)=P(Z>1.16)=1-0.8643\\P(X>121)=0.137\\[/tex]

Thus the answer will be 0.137.

Answer:

19

Step-by-step explanation:

10 + 9 = 19. If you look at how many students are above the "30 mark", you will count 10 on the first bar and 9 on the second.

Answer:

This demonstrates the associative property of addition which states that a + (b + c) = (a + b) + c. Basically, it states that it doesn't matter which order you add numbers in, you will always get the same result.

Answer:

x ≤ 3

we have to transpose -7 from left to right

Answer:

X/y = 2/5

Y= x+12

Where y = students

X= adults

Number of adults= 8

Number of students= 20

Step-by-step explanation:

The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults.

Let adult be x

Let student be y

X/y = 2/5

5x= 2y.... equation one

Y= x+12..... equation two

Substituting equation two into equation one

5x= 2(x+12).

5x = 2x +24

3x= 24.

X= 8

Y= x+12

Y= 8+12

Y= 20

Number of adults= 8

Number of students= 20

Joanne has to pay monthly membership fees = $24.72 per month

And registration fee = $49.95

Here,

The given expression is 24.72 m + 49.95

Joanne has to pay registration fee as well as monthly membership.

And, m denotes the number of months.

We have to explain the different part of given expression.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Now,

The given expression is ;

⇒ 24.72 m + 49.95

Joanne has to pay registration fee as well as monthly membership.

Where, m denotes the number of months.

From the expression;

⇒  24.72 m + 49.95

We can see that,

Joanne has to pay monthly membership fees = $24.72 per month

And registration fee = $49.95

To learn more about linear expression visit:

https://brainly.com/question/12788590

#SPJ2

Answer:

[tex]\huge\boxed{(2x+8)(x-3)=2x^2+2x-24}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2x+8)(x-3)=(2x)(x)+(2x)(-3)+(8)(x)+(8)(-3)\\\\=2x^2-6x+8x-24\qquad\text{combine like terms}\\\\=2x^2+(-6x+8x)-24\\\\=2x^2+2x-24[/tex]

Answer:

2x^2+2x-24

Step-by-step explanation:

when you see two parentheses, you should first think : FOIL!

you take the First terms in each of the parentheses which is 2x and x and multiply them. (2x^2)

then you take the Outer terms in the parenthesis which is 2x and -3 and multiply them. (-6x)

then you take the Inside terms which is +8 and x and multiply them. (+8x)

lastly, you take the Last terms which is +8 and -3 and multiply them. (-24)

you should get this : 2x^2-6x+8x-24. combine like terms and there's your answer!

i also advise you to write down all your terms until you are familiar with this foil stuff. don't be ashamed if you need to write them down! you'll get the hang of it! :)

Answer:

a. x = -2

Step-by-step explanation:

64ˣ = 16⁽ˣ⁻¹)

64 = 4³

16 = 4²

4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)

4³ˣ = 4²ˣ⁻²

3x = 2x - 2

x = -2

Answer:

[tex]\huge \boxed{x=-2}[/tex]

Step-by-step explanation:

64^x = 16^(x-1)

Rewrite the bases with base of 4.

(4^3)^x = (4^2)^(x-1)

Multiply exponents.

4^(3x) = 4^(2(x-1))

Cancel same bases.

3x = 2(x-1)

Expand brackets.

3x = 2x - 2

Subtract 2x from both sides.

x = -2

Answer:

x=14

Step-by-step explanation:

1[tex]\sqrt{x+2}[/tex] +2 = 6 --------------- put nums on 1 side

1[tex]\sqrt{x+2}[/tex] = 4 -------------------by the way, 1

[tex]\sqrt{x+2}[/tex]  =4 ------------- square both sides

x+2 = 16 --------------- subtract 2 from both sides

x = 14

Answer:

Step-by-step explanation:

Using the distance formula

the distance between (-10, 12) and (5, 3) is

d = 17.492855

We have the final answer as

Hope this helps you

Answer:17.5

Step-by-step explanation:

Answer: The number 99.4177 rounded to the nearest hundredth is 99.42.

Step-by-step explanation:

Here's how I got my answer:

Since you need to round to the nearest hundredth, then round to the first two decimal places. So if the number is 5 or greater, then round up. If the number is 4 or lesser, then do not round up.

In this scenario:

99.4177

Round the 1 in the hundredths place up to 2, because 7 is on the greater end. Since they are just asking you for the hundredths place, then do not round anything else.

Hence, your final answer is 99.42.

Answer:

4d+56

Step-by-step explanation:

4(d+14)       you must do distributive property to simplify this answer.

4d + 56      after distributing remove parentheses

Answer:

(4, 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 11 → (1)

x - 3y = 1 → (2)

Adding (1) and (2) term by term will eliminate the term in y

3x = 12 ( divide both sides by 3 )

x = 4

Substitute x = 4 into either of the 2 equations and evaluate for y

Substituting into (1)

2(4) + 3y = 11

8 + 3y = 11 ( subtract 8 from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Solution is (4, 1 )

Answer:  x = 34

Step-by-step explanation:

⁴ ⁻ˣ/₅ + ˣ + 2/₃ = 6

Now resolve into fraction and convert to a linear equation

4 - x /₅ + x + 2/₃ = 6

3( 4 -x ) + 5( x + 2 )/15 = 6

3( 4 - x ) + 5( x + 2 )    = 6 x 15

12 - 3x + 5x + 10         = 90

        2x + 22              = 90

                             2x  = 90 - 22

                             2x  = 68

                                x = 34