Can someone show me an example of long division?

Answer:

Step-by-step explanation:

[tex]\int 3x(x^2+3)^4 \ dx[/tex].

It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.

Integration by substitution involves swapping the variable [tex]x[/tex] for another variable which depends on x: [tex]u(x)[/tex]. (We are going to choose [tex]u[/tex] for this question).

The very first step is to choose a suitable substitution. That is, an equation [tex]u=f(x)[/tex] which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution [tex]u=\text{The Term}[/tex].

Your integral contains the term [tex]x^2 + 3[/tex]. The derivative is [tex]2x[/tex] and (ignoring the constants) we see [tex]x[/tex] is also in the integral and so the substitution [tex]u=x^2+3[/tex] will unravel this integral!

Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").

[tex]u=x^2+3 \Rightarrow \frac{du}{dx}=2x \Rightarrow dx = \frac{1}{2x} du[/tex]

Then,

[tex]\int 3x(x^2+3)^4 \ dx = \int 3x \cdot u^4 \cdot \frac{1}{2x} du = \int \frac{3}{2}u^4\ du[/tex].

The substitution has made this integral is easy to solve!

[tex]\int \frac{3}{2}u^4\ du= \frac{3}{10}u^5 + C[/tex]

Finally we can substitute back to get the answer in terms of x:

[tex]\int 3x(x^2+3)^4 \ dx = \frac{3}{10}(x^2+3)^5+C[/tex]

Answer:

The slope is -1/3

Step-by-step explanation:

We can find the slope of a line using the formula

m = (y2-y1)/(x2-x1)

  = (2-3)/(3-0)

  = (-1/3)

  =-1/3

Answer:

m= -1/3

Step-by-step explanation:

Slope is determined from the formula:

y2-y1/x2-x1

Input the corresponding numbers in the formula.

2-3/3-0

-1/3

m= -1/3

simplify to get 1/3 times 17/4 which simplifies to 17/12 or 1 and 5/12.

Answer:

17/12

Step-by-step explanation:

1/3 x 4 1/4 change to

1/3 x 17/4

multiply the top and then the bottom : 17/12

balance = $360

2% of balance = 0.02*360 = 7.20

Since $10 is larger than $7.20, this means the min monthly payment is $10

Answer: 10

Answer:

BC = 6.7 cm (rounded to nearest tenth)

Explanation:

Given: ABC is a right triangle with right angle C as shown below.

Side AB=18 cm and m∠A=22°.

Using Sine ratio in triangle ABC to find BC.

Sine ratio is defined as the ratio of the opposite side of a right triangle to the hypotenuse.

i.e

[tex]\sin A = \frac{Opposite side}{Hypotenuse side}[/tex]

Let BC = x (opposite side) and AB = 18 cm(Hypotenuse side)

then;

 [tex]\sin 22^{\circ} = \frac{x}{18}[/tex]

[tex]0.37460659341 = \frac{x}{18}[/tex]

Multiply both sides by 18 we get;

[tex]x = 0.37460659341 \times 18 = 6.74291868[/tex]

therefore, value of BC (nearest tenth place) is, 6.7 cm

Answer: 6.7cm

Step-by-step explanation: I took the K12 test.

Answer:

12/35

Step-by-step explanation:

"2fifth" = 2/5

"6seventh" = 6/7

"times" = *

Multiply across:

(2/5) * (6/7) = 12/35

12/35 is your answer

~

Answer:

12/35

Step-by-step explanation:

2/5 times 6/7

First multiply the numerators.

2 x 6 = 12

Then multiply the denominators.

5 x 7 = 35

Your answer is 12/35

Answer:

A discrete graph

Step-by-step explanation:

It would make sense because you can track the distances on the coordinate plane

Answer:

The first graph or A.

Step-by-step explanation:

[tex]\text{l-length}\\\text{w-width}\\lw-area\\108\ m^2-area\\d-diagonal\\\\\text{The equation}\ \#1:\\\\lw=108\to l=\dfrac{108}{w}\\\\\text{The equation}\ \#2:\\\\\text{Use the Pythagorean theorem:}\\\\l^2+w^2=d^2\to l^2+w^2=15^2\to l^2+w^2=225\\\\\text{Subtitute from}\ \#1\ \text{to}\ \#2:[/tex]

[tex]\left(\dfrac{108}{w}\right)^2+w^2=225\\\\\dfrac{11,664}{w^2}+w^2=225\qquad\text{multiply both sides by }\ w^2\neq0\\\\11,664+w^4=225w^2\qquad\text{subtract}\ 225w^2\ \text{from both sides}\\\\w^4-225w^2+11,664=0\qquad\text{substitute}\ t=w^2 > 0\\\\t^2-225t+11,664=0\\\\\text{use the quadratic formula or solve by factoring}.\\\\t^2-144t-81t+11,664=0\\\\t(t-144)-81(t-144)=0\\\\(t-144)(t-81)=0\iff t-144=0\ or\ t-81=0\\\\\boxed{t=144}\ or\ \boxed{t=81}\to w^2=144\ or\ w^2=81\\\\w=\sqrt{144}\ or\ w=\sqrt{81}\\\\\boxed{w=12\ m}\ or\ \boxed{w=9\ m}[/tex]

[tex]\text{Put the values of}\ w\ \text{to the equation}\ \#1:\\\\l=\dfrac{108}{12}\to\boxed{l=9\ m}\ or\ l=\dfrac{108}{9}\to\boxed{l=12}\\\\\text{The formula of a perimeter of a rectangle:}\\\\P=2l+2w\\\\P=2(12)+2(9)=24+18=42\\\\Answer:\ \text{The perimeter of the rectangle is equal 42 m}.[/tex]

The perimeter of the rectangle is 42m.

To find the perimeter of the rectangle, we need to know the lengths of its sides. From the given information, we know that the area of the rectangle is 108m^2 and its diagonal is 15m. We can use this information to find the lengths of the sides.

Let the length of the rectangle be 'l' and the width be 'w'.
Given, lw = 108 and sqrt(l^2 + w^2) = 15.
Squaring both sides of the second equation, we get l^2 + w^2 = 225.
Since lw = 108, we can solve the quadratic equation l^2 - 108l + 225 = 0 to find l. In this particular case, the quadratic factors as (l - 9)(l - 12) = 0, so l = 9 or l = 12.
Substituting the values of l in the equation lw = 108, we find w = 12 or w = 9.
Since the perimeter is the sum of all the sides, the perimeter of the rectangle is (2l + 2w) = (2 * 9 + 2 * 12) = 42m.

The SSE for the data set is:  24

The data points are given by:

        (3,6),(6,2),(9,10)

The data points are as follows:

when x=3   y=6

when x=6   y=2

and when x=9   y=10

Also, the line of best fit is as follows:

[tex]y=\dfrac{2}{3}x+2[/tex]

The SSE( sum of square for error ) is calculated as follows:

when x=3

from the line of best fit we have: y=4

when x=6

then y=6

when x=9

then y=8

when x=3        6-4= -2

when x=6       2-6= -4

and when x=9      10-8=2

Hence, the square of these difference quantity is:

(-2)²=4

(-4)²=16

and (2)²=4

Hence, the sum of these square quantity is: 4+16+4=24

Hence, the SSE of data is:  24

We have the supplementary angles.

The sum of the measures of the two Supplementary Angles is 180°.

Therefore we have the equation:

13x - 2 + 39 = 180

13x + 37 = 180     subtract 37 from both sides

13x = 143      divide both sides by 13

x = 11

Step-by-step explanation:

We are given the co-ordinates,

x : -2, -1, 0, 1, 2

y : 8, 5, 2, -1, -4

According to the graph, we see that this function represents a straight line.

The general form of the straight line is y = mx + c, where m is the slope and c is the y-intercept.

So, taking any two points we will find the equation of the straight line.

Consider, (0,2) and (1, -1). Now, slope is given by,

m = [tex]\frac{-1-2}{1-0}[/tex]

i.e. m = -3

Now, we will find the y-intercept of this equation using (0,2) and m = -3,

i.e. y = -3x + c

i.e. 2 = c

Hence, the equation of the straight line is y = -3x + 2.

Answer:

The correct answer on Odyssey is Ellipse

Step-by-step explanation:

I got it correct on Odyssey

Answer:   b - 8  is what i believe the answer is make sure tho im only in 6 th grade Step-by-step explanation:

Answer:

It would be C

Answer:

x = 4

Step-by-step explanation:

distribute both parenthesis on the left side of the equation

6 + 3x - 2x - 1 = 9

x + 5 = 9 ( subtract 5 from both sides )

x = 4

Answer:

c ÷ 7 + 5 = 8

Step-by-step explanation:

The Translate the sentence into an equation is c/7 +5 =8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

given variable is given as c therefore, the translation of the given equation  Five more than the quotient of a number and 7 is equal to 8 will be :

c/7 +5 =8

Therefore, the Translate the sentence into an equation is c/7 +5 =8.

Read more about equations at :

https://brainly.com/question/10413253

#SPJ2

The equation representing the total cost after buying x slices of pizza

is [tex]\( C(x) = E + x \times P \)[/tex].

Let's denote the entrance fee as E (in dollars) and the cost of each slice of pizza as P (also in dollars). Given the problem, we can write the following equations based on the given information:

After having 1 slice of pizza, the total cost is $6:

[tex]\(E + 1 \times P = 6\)[/tex]

After having 2 more slices of pizza (total 3 slices), the total cost is $10:

[tex]\(E + 3 \times P = 10\)[/tex]

To find the equation that represents the total cost (y) after buying x slices of pizza (let's call it C(x), we need to generalize the pattern observed in the given equations.

Notice that the entrance fee remains constant regardless of the number of slices of pizza bought. So, we can write the equation as:

[tex]\[ E + x \times P = C(x) \][/tex]

Substituting the values given in the problem:

[tex]\[ C(x) = E + x \times P \][/tex]

So, the equation representing the total cost after buying x slices of pizza

is [tex]\( C(x) = E + x \times P \)[/tex]. This equation gives the total cost (y) as a function of the number of slices of pizza bought (x).

10b+6=7b-6.

3b=-12

b=-4.

*Note that you can just divide by 12 on both sides to simplify the equation.

Answer:

10 possible outcomes

Step-by-step explanation:

- One coin has two sides (heads and tails)

- It is tossed 5 times

- 2 times 5 is 10

Answer:

49.5

Step-by-step explanation:

76-42+65 is 99, the you divide by 2, and that is 49.5

The student that solved at a rate of 28 per minutes was Logan

Answer:

Logan

Answer:

Logan solved problems at a rate of 28 problems per minute.

Step-by-step explanation:

To find the number of problems per minute that a person solved, you will divide the number of problems that they solved by the number of minutes that they took.

Murray:

58 problems in 2 minutes,

58 / 2 = 29

He solved problems at a rate of 29 problems per minute.

Kris:

78 problems in 3 minutes,

78 / 3 = 26

He solved problems at a rate of 26 problems per minute.

Logan:

84 problems in 3 minutes,

84 / 3 = 28

He solved problems at a rate of 28 problems per minute.

Since you found that Logan solved problems at a rate of 28 problems per minute, Logan is the student that solved problems at a rate of 28 per minute.

Answer:

36 ft

Step-by-step explanation:

So the proportion of the big triangle is 48:4 or 12:1. So if the small triangle’s height is 3 feet, then 3*12 is 36 feet.

Answer: 36 ft

Step-by-step explanation:

Similar triangles means there is a constant proportion between the left legs, the base legs, and the hypotenuses.

[tex]\frac{LeftLeg(large)}{LeftLeg(small)}= \frac{BaseLeg(large)}{BaseLeg(small)}[/tex]

                  [tex]\frac{x}{3}= \frac{48}{4}[/tex]

Cross multiply: x(4) = 3(48)

solve for x:        ÷4     ÷4    

                          x    =  3(12)

                                =  36

Answer:

$4,461.60

Step-by-step explanation:

Answer:

.42

Step-by-step explanation:

Since we are rounding to the 2, we will look at the digit after it

4 < 5 so we leave the 2 alone

.424 is rounded to .42

Answer:

0.42 is your answer

Step-by-step explanation:

The underlined number is 2. Look at the place value to the right. It is a 4. Because 4 is less than 5, round down.

0.424 rounded to the nearest hundredth place is 0.42

~

Answer:

I graphed it and u can find the two solutions :)

Step-by-step explanation:

Answer:

12 x 2 = 24

24 x 3 = 72

72 x 4 = 288

288 x 5 = 1440

The result of each multiplication is being multiplied by the next consecutive number so the pattern is = x2,x3,x4,x5.

Step-by-step explanation:

Boom

Final answer:

An acrostic poem for the word 'percent' is crafted with each line pertaining to the process and concept of calculating percents, expressed as a part of 100, or ratios with a denominator of 100.

Explanation:

An acrostic poem for the word percent could be:

Perusing numbers, calculations at hand,

Every figure is neatly planned.

Ratios and fractions - they all fit,

Calculations to make you think a bit.

Each part of a hundred, clearly set,

Numerical values that we get,

Twenty, fifty, seventy-five, all to percent we convert and drive.

This acrostic poem takes the word percent and creates a line for each letter that relates to the concept of percentages, which are ratios with a denominator of 100. Calculating percents involves setting up equivalent fractions or converting to decimals and fractions for ease of use in various mathematical situations. An understanding of this concept is essential for mathematical proficiency.

Answer:

The answer would be 484

Step-by-step explanation:

Step 1: Multiply the length, width, and height.

11x11x12=1452

Step 2: Divide by 3

1452/3=484