21-25 Use the form of the definition of the integral given in Theorem 4 to evaluate the integral.
23. [tex]\int_{-2}^{0}\left(x^{2}+x\right) d x[/tex]

Answers

Answer 1

[tex]\displaystyle \int^0_{-2} (x^2 +x )~dx\\\\\\=\displaystyle \int^0_{-2} x^2~ dx +\displaystyle \int^0_{-2}x ~ dx\\\\\\=\dfrac 13 \left[x^3 \right]^{0}_{-2}+ \dfrac 12 \left[ x^2\right]^{0}_{-2}\\\\\\=\dfrac 13 (0+8) + \dfrac 12 (0-4)\\ \\\\=\dfrac 83 - \dfrac 42\\\\\\=\dfrac 83 - 2\\\\\\=\dfrac 23[/tex]


Related Questions

For two functions, f(x) and g(x), a statement is made that f(x) = g(x) at x = 5. What is definitely true about x = 5?

A. Both f(x) and g(x) cross the x-axis at 5.
B. Both f(x) and g(x) cross the y-axis at 5.
C. Both f(x) and g(x) have a maximum or minimum value at x = 5.
D. Both f(x) and g(x) have the same output value at x = 5

Answers

Answer:

D

Step-by-step explanation:

f(x) = g(x) at x=5

means

f(5) = g(5)

Simplify this expression . With each step. please (x2 - x - 2)/(x2 + 5x + 4)

Answers

Answer:

I hope dis helps

Step-by-step explanation:

Simplify  

           x2 + 5x + 4

Trying to factor by splitting the middle term

1.1     Factoring  x2 - x - 2

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   -1 .

     -2    +    1    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  1

                    x2 - 2x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-2)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-2)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-2)

            Which is the desired factorization

Trying to factor by splitting the middle term

1.2     Factoring  x2+5x+4

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +4

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   5 .

     -4    +    -1    =    -5

     -2    +    -2    =    -4

     -1    +    -4    =    -5

     1    +    4    =    5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  4

                    x2 + 1x + 4x + 4

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+1)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x+1)

            Which is the desired factorization

Canceling Out :

1.3    Cancel out  (x+1)  which appears on both sides of the fraction line.

Final result :

 x - 2

 —————

 x + 4

please help !! I dont know what the awnser is, i put mean, medium, and mode for the first try adn it gave me partial

Answers

Answer:

All of them but the last one

Step-by-step explanation:

How would I solve I need to know Asap and what is the answer

Answers

Answer:

All of them are true.

Step-by-step explanation:

The symbol ≅  is used to show congruence between two shapes.

Congruency means that the shapes have the same shape and size.

This means that the two shapes are the same.

This means that all sides are going to be the same, so the first two statements are true.

This also means that the angles are the same, so the last two statements are also true.

mark brainliest please!

Answer:

1 and 3 are correct.

Step-by-step explanation:

You can just look at the order of the letters in the triangle congruence statement and see if they correspond with the answer choices.

For example... OC is congruent to JA because for both segments, it's the first letter, then the second letter from the beginning triangle congruence statement.

Pleaseeee answer I’ll give you pointsss

Answers

Answer:

Okay . That looks interesting. Can't help.

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.

Answers

Step-by-step explanation:

[tex]4(2 - x) > - 2x - 3(4x + 1)[/tex]

[tex]8 - 4x > - 2x - 12x - 3[/tex]

[tex]8 - 4x > - 14x - 3[/tex]

[tex] - 4x + 14x > - 3 - 8[/tex]

[tex]10x > - 11[/tex]

[tex]x = - 1.1[/tex]

Answer:

[tex]x > \frac{-11}{10}[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]4(2 - x) > -2x - 3(4x + 1)[/tex]

[tex](4*2)+(4 * (-x)) > -2x + (-3 * 4x) + (-3 * 1)[/tex]

[tex]8 - 4x > -2x - 12x - 3[/tex]

Step 2:  Combine like terms

[tex]8 - 4x > (-2x - 12x) - 3[/tex]

[tex]8 - 4x > -14x - 3[/tex]

Step 3:  Add 14x to both sides

[tex]8 - 4x + 14x > -14x - 3 + 14x[/tex]

[tex]8 + 10x > -3[/tex]

Step 4:  Subtract 8 from both sides

[tex]10x + 8 - 8 > -3 - 8[/tex]

[tex]10x > -11[/tex]

Step 5:  Divide both sides by 10

[tex]\frac{10x}{10} > \frac{-11}{10}[/tex]

[tex]x > \frac{-11}{10}[/tex]

Answer:  [tex]x > \frac{-11}{10}[/tex]

Please help I really need this

Answers

Answer:

(0 , 4)

Step-by-step explanation:

The Y-intercept is when a line crosses sector y at any point. This means x will be zero. Simply to find the y-intercept from this quadratic function, just look at where the line crosses the y-line.

This clearly passes at (0,4), therefore (0,4) is the y-intercept.

Darcy pays $37.95 for a 25.3-kilometer taxi ride.

How much does Darcy pay, in dollars, per kilometer?

Answers

Answer:

1.5 per kilo

Step-by-step explanation:

Answer: That would be $1.50

Explanation: I took a test and I got it right

find the derivative pls !!

Answers

The answer d/ds(5/2(s^2-1)(s^3+5))
=5/2s(5s^3-3s+10)

whats 1 added up to 1?

Answers

4 dude lol just playin 2

Molly's alarm clock fell to the floor and the glass face was broken. Molly measured the glass face so that she could order a new one.

The radius of the circle-shaped glass face is 8 centimeters. What is the approximate area of the glass face? (Use 3.14 for .)

Answers

Answer:

200.96 cm^2

Step-by-step explanation:

πr^2 is the formula for the area of a circle

π*8^2

64π

substitute pi with 3.14

64 * 3.14 = 200.96

200.96

mark brainliest please!

SOLVE PLSEEE I GIVE POINTS

Answers

Since the diameter for a segment is 68 centimeters long, we must divide that number by 4, since there are four circles. Next, we get 17.

Then, we use the formula for solving a circle, which is [tex]A = \pi r^2[/tex]. Plug in 8.5 (half of 17) for the radius, and then convert pi into 3.14. The equation should now look something like this: [tex]A = 3.14 * 8.5^2[/tex]. When solving, we get 265.865 for one circle only. We next multiply 256.856 by 4 since there are four circles. After multiplying you should get a total of 907.46 centimeters squared.

If this isn't correct, then do the same thing, but the radius is 34 centimeters.

The regular price of a sofa, in dollars, is represented by . The sale price of the sofa is 30%off the regular price. Select alltrue statements.
A. The sale price of the sofa can be represented by −0.3.
B. The sale price of the sofa can be represented by 0.7.
C. The sale price of the sofa can be represented by 0.3
D. The dollar amount of the discount for the sale price can be represented by 0.3.
E. The dollar amount of the discount for the sale price can be represented by −0.3.

Answers

Answer:

BE

Step-by-step explanation:

The sale price of the sofa is given as :

Original Price (100% - 30%)Original Price (70%)Original Price (0.7)

The dollar amount for the discount

- 30% [discount]-0.3

8 ≤ 2m Find variable of m

Please show your work

Answers

Answer:

m ≥ 4

Step-by-step explanation:

8 ≤ 2m

8/2 ≤ m

4 ≤ m

m ≥ 4

2x +2y-16x+4y+20=0 solve by completing the square​

Answers

Answer

7/3

Step-by-step explanation:

Find f of x and f of y

F(x,y) = 2x + 27 - 16x + 4y + 20, f of x = -14

F(x,y) = 2x + 2y - 16x + 4y + 20, f of y = 6

Find the fist partial derivative

f of x = -14

f of y = 6

Subsitude f of x = 14 and f of y = 6 into dy/dx = - f of x / f of y

reduce the fraction

dy/dx = - 14/6 = - - 7/3 = 7/3

Question in picture below

Answers

Answer:

  f(x) = 3sin(3.1416(x +4)/7)

Step-by-step explanation:

You want the equation of a sine function with an amplitude of 3 and having one cycle between the points (-11, 0) and (3, 0), where it has negative slope.

Equation

The equation will generally be of the form ...

  f(x) = (amplitude)·sin(2π/(period)·(x-(horizontal translation)))

Application

Here, the amplitude is 3 units, the period is (3 -(-11)) = 14 units, and the horizontal translation from the origin to the positive-going midline crossing is 4 units to the left.

Then f(x) is ...

  f(x) = 3·sin(2π/14(x -(-4))

  f(x) = 3·sin(3.1416/7(x +4))

<95141404393>


(a) Is the image
of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.

Answers

I will have to see the image I am pretty right

Mrs. Murray wants to hang lights around the edge of the ceiling. The ceiling measures 14.5 feet by 9.6 feet. What is the perimeter, in feet, of Mrs. Murray's ceiling?
What is the perimeter of the ceiling in inches.

Answers

Answer:

48.2 feet

or

578.4 inches

Step-by-step explanation:

Perimeter is the distance around the shape or in this case the room. Assuming the room is a rectangle you would have two walls of the same length totaling 4 walls.

To find the perimeter add up 14.5 + 14.5 + 9.6 + 9.6 = 48.2 feet

Since it askes for the answer in inches you have to convert from feet to inches by multiplying your answer by twelve.

To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size?

4.5 < c < 12
4.5 ≤ c ≤ 12
c < 4.5 or c > 12
c ≤ 4.5 or c ≥ 12

Answers

Answer:

last one is the answer of the following question

Answer:

D

Step-by-step explanation:

Solve the following equation

Answers

Answer:

Write it down in comments i can barely see

Step-by-step explanation:

Can yall help me with this math

Answers

Answer:

2 the change in expected height for every additional centimeter of femur length

Step-by-step explanation:

1 and 4 have 55 is the starting point but is just there to throw you off and 3 has expected femur length, but the graph says expected height

Mean:median:mode:range

Answers

Answer: Hi there ^^ oki so ima explain what these are/mean
So for starters this is used in math and isnt really useful but u got to do the work sadly so.
the mean is the arithmetic average of a set of given numbers.
the median is the middle in sorted numbers (after u sort the given numbers), ascending or desending, list of numbers can be more descripited of that data set than the average.
the mode is the value that appears most frequently, for example "the mode of {4,2,4,3,2,2} is 2 because it accurs 3 times, so in short words the mode is the number used the Most,
And lastly the Range is the differance between the highest and the lowest values in a set of numbers.

i hope this helps u out! ^^ ~xlXCherryColaXlx

What is the surface area of the cylinder with height 3 yd and radius 4 yd? Round your
answer to the nearest thousandth.

Answers

A≈175.93yd²

A=2πrh+2πr2=2·π·4·3+2·π·42≈175.92919yd²

Therfore the surface area of the cylinder with height 3 yd and radius 4 yd is 175.93

A coin tossed four times and a card is selected from a standard deck of cards

Answers

Probability of landing on tails = 1/2Probability of choosing a spade = 1/4, as there are 13 spades in a pack of 52 cardsSo the probability of both = 1/2 * 1/4 = 1/8.We are assuming the deck of cards does not contain jokers.

What is the length of the hypotenuse of the triangle below?
45
h
45°
5√2
90⁰
5√2

Answers

Answer:

10

Step-by-step explanation:

find the square root of the sum of the squares

The length of the hypotenuse for the given right angled triangle is 10 units.

What is a Pythagoras theorem?

Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.

We can write the formula for Pythagoras theorem as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is to find the length of the hypotenuse in the right angled triangle shown.

Using the Pythagoras theorem, we can write that -

(hypotenuse)² = (base)² + (perpendicular)²

(hypotenuse)² = (5√2)² + (5√2)²

(hypotenuse)² = 2 x (5√2)²

(hypotenuse)² = 2 x 25 x 2

(hypotenuse)² = 100

(hypotenuse) = 10

Therefore, the length of the hypotenuse for the given right angled triangle is 10 units.

To solve more questions on triangles, visit the link-

https://brainly.com/question/2773823

#SPJ7

Describe a set of transformations that would map Triangle FGH onto Triangle F’G’H’

Answers

The translations would be this

1) reflection over the x-axis
2) translation of (-6,0)

the table shows the fees david charges for yard work

how much does david charge for yard work that takes 4.5 hours​

Answers

157= one hundred and fifty seven

Can any math experts please help me out with this? Thank you,

Answers

Answer:

13) x = 19

14) x = 12.4

Step-by-step explanation:

So, for 13, we know that the whole thing is 90 degrees, a right angle.

So, (4x - 17) + 31 = 90

Now, we'll subtract 31 from 90 to figure out the other angle.

4x - 17 = 59

Now, add seventeen to both sides to get 4x alone...

4x = 76

Divide each by four!

x = 19

Now, to check, we plug this x value into our first equation:

(4(19) - 17) + 31 = 90

(76 - 17) + 31 = 90

(59) + 31 = 90

90 = 90 :: true!

________________________________________

For 14, we know that the total must be 180, because it's a straight angle.

So, (5x + 22) + 96 = 180  
Again, subtract the known angle from each side:

5x + 22 = 84

Subtract 22 from each side to get the exponent by itself...

5x = 62

Divide each side by 5:

x = 12.4

Now, plug it in to check.....

(5*12.4) + 22 + 96 = 180

62 + 22 + 96 = 180

84 + 96 = 180

180 = 180 :: true!

coulddd i be helped really quick?

Answers

Answer for 4 is 56 costumers
Answer for 30 is x+56=y-$5.05
Cover charge be xCustomers be y

So

For every increase in cover price of x means 5x+0.5 decreases customers by 30

So

the expression is

5x+0.5=300y-305x=300y-30.5300y=5x-30.55x-300y-30.5=0

Trey plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.

Answers

Answer:

2n*m. when there is a one in front of a letter, it is immediately just the letter

If there are 12 months (m) and he plans to watch 2 per month, we will just multiply 2(12) and it gets us with 24 movies. If the amount of months is lower than 12, we can just put 2(m)
Other Questions
__________ is a narrative presentation analyzing the internal and external environment of an organization and its publics as it relates to the start of a campaign or program. what is the difference between chasing and pursuingis chasing one sided where pursuing is reciprocated? Carbohydrates are found in many foods. What is the end result of the bodys use of a carbohydrate? Let x = a bi and y = c di and z = f gi which statements are true? check all of the boxes that apply. x y = y x (x y) z = x (y z) x y = y x (x y) z = x (y z) (x y) z = x (y z) you do 185 J of work in 45 seconds. how much power do you use? _________________ conceded that our brains process and react to vast amounts of information without our conscious awareness. Discuss several techniques for managing stress in your life. 4. Why did Japan attack the United States at Pearl Harbor? What had the United States done thatmade them believe it was necessary? lux73336004/21/2020EnglishMiddle SchoolansweredThe picture shows Felix the Cat. Read the blog that follows.Felix the Cat is wrapped in spaghetti while trying to eat it. Tasneems Tales Have you ever been confused and just didnt know what to do? Have you ever found yourself tied in knots over a problem? Well, this blog is for you. Well teach you stuff you never learned but should have, such as: how to really tie your shoelaces. the secret to eating spaghetti. what to do with the cat fur on your clothes. what to not to do on your first date.What is the most important purpose of the cartoon in this blog?A) to show how to eat spaghettiB) to entertain the readerC) to show a cat tied in knotsD) to show bad table etiquette Do we as a society take white collar crime seriously enough? How should it be punished/deterred? Water is able to act as an acid in some reactions.T/F Unlike the United States, most countries across the globe rely on the ________ system to measure units, creating problems for both buyers and sellers in the international marketplace A set of beliefs about the superiority of one racial or ethnic group compared to another is What percentage of times are between 6 and 22 hours?16%68%95%99.7% What does the gerund phrase "volunteering at the animal shelter" contribute to the text? the phrase conveys significant interest and variety. the phrase adds a specific detail about time and place. the phrase acts as a noun that is the subject of the sentence. the phrase adds more details by providing a direct object. A lie detector test is not really accurate claim or counterclaim a trapezoid has a base of 32 inches and 14 inches and a height of 25 inches Why did women attempt to use the 14th Amendment to secure their right to vote? Evidence shows that some grasses benefit from being grazed. Which of the following terms would best describe this plant-herbivore interaction?a) parasitismb) commensalismc) mutualismd) competition Find three different ways to write the number 437000 as a multiple of a power of 10