Simplify each expression. Select the correct answer from the drop-down menu.

−6(3i)(−2i) =


2(3 − i)(−2 + 4i) =

Answers

Answer 1

Answer:

Step-by-step explanation

-6(3i)(-2i)=-6(3i*-2i)=-6*-6i²=36i²

2(3-i)(-2+4i)=(6-2i)(-2+4i)=-12+24i+4i-8i²=-8i²+28i-12

Answer 2

Answer:

1. -36

2. -4+28i

3. 10+8i

Step-by-step explanation:

EDGE2022


Related Questions

For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.

Answers

The equation 15x + 5y = 0  is a direct variation and the constant of variation is -3 while the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation

How to categorize the type of each equation?

As a general rule, we have the following forms of equation:

Direct variation: y =kx

Inverse variation: y = k/x

Where k represents the constant of variation

The equations 15x + 5y = 0 can be rewritten as:

5y = -15x

Divide by 5

y = -3x

The above equation take the form y = kx

This means that k = -3

Hence, the equation 15x + 5y = 0  is a direct variation and the constant of variation is -3

However, the equation -5x + 8y = 3 do not take any of the given forms

Hence, the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation

Read more about variation at:

https://brainly.com/question/12381371

#SPJ1

Consider the parametric equations below.
x = t^2 − 3, y = t + 2, −3 ≤ t ≤ 3
Eliminate the parameter to find a Cartesian equation of the curve.
for
−1 ≤ y ≤ 5

Answers

Solve the second equation for [tex]t[/tex], then substitute it into the first equation.

[tex]y = t + 2 \implies t = y-2[/tex]

[tex]x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}[/tex]

WILL GIVE BRAINLIEST

Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.

1. x2 + 6x - 7

2. x2 - 5x + 6

3. x2 - 6x - 7

4. x2 + 5x - 6

5. x2 + x - 12

6. x2 - 2x - 8

7. x2 - 4x - 5

8. x2 + 2x - 3

9. x2 - 16

10. x2 - x - 12

11. x2 -9x + 18

12. x2 -5x - 14

13. x2 - 7x + 10

14. x2 -11x + 24

15. x2 - x - 30

Answers

Factorization refers to the process by which the terms that are common in an expression are obtained.

What is factorization?

Factorization refers to the process by which the terms that are common in an expression are obtained.

Given the trinomials, the correct binomial factors are;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

Learn more about factorization:https://brainly.com/question/4335007

#SPJ1

What's the Value of X in 1/2 + X = 5/6

Answers

Answer:

x = 1/3

Step-by-step explanation:

1/2 + X = 5/6

collecting the like terms

X = 5/6 - 1/2

making one fraction on the left side by taking the common denominator

X = (5 - 3)/6

X = 2/6

devide the numerator and denominator by 2, you get

X = 1/3

Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)

Answers

When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).

We are required to divide the first expression by second expression.

Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.

Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.

We know that  relationship between quotient, divisor, divident and remainder is as under:

Dividend=Divisor*Quotient+Remainder

[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39

Quotient=[tex]x^{2} +8x+19[/tex]

Remainder=39

Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

Learn more about division at https://brainly.com/question/25289437

#SPJ1

Which expression represents seven less than the product of thirteen times a number, and two squared?

(13x + 22) · 7

7(13x · 22)

7 + 13x + 22

7 + 13x · 22

(13x · 22) − 7

Answers

Seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

How to represent an expression?

The expression says  seven less than the product of thirteen times a number, and two squared.

Let

the number  = x

Hence, the product of thirteen times a number, and two squared is as follows:

13(x)(2²)

Therefore,  seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

learn more on expression here: https://brainly.com/question/14172188

#SPJ1

What are the first five terms in the recursive sequence defined by the following? (only one is correct)

a1= 1

a2=1

an= an-2+an-1

a) {1,1,2,3,5}

b) {1,1,0,-1,-1}

c) {2,3,5,8,13}

d) {1,-1,2,-3,5}

Answers

Answer:

d 1-12-3-5 is the answer

The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.


Drag each function to show whether it has roots at x=−2 and x=3, roots at x=2 and x=−3, or neither.

Answers

The following classification of quadratic equations is presented below:

x = - 2 and x = 3: h(x) = (x + 2) · (x - 3), k(x) = - 3 · (x + 2) · (x - 3). x = 2 and x = - 3: g(x) = 8 · (x + 3) · (x - 2), m(x) = (x + 3) · (x - 2). Neither: j(x) = (x - 2) · (x - 3)

How to classify quadratic equations in terms of its roots

In this problem we have quadratic equations in factored form, whose form is presented below:

y = a · (x - r₁) · (x - r₂)      (1)

Where r₁ and r₂ are the roots of the equation and a is the leading coefficient. A value of x is a root if and only if y is zero. Besides, we must located all the quadratic equations according to their roots.

x = - 2 and x = 3

h(x) = (x + 2) · (x - 3)

k(x) = - 3 · (x + 2) · (x - 3)

x = 2 and x = - 3

g(x) = 8 · (x + 3) · (x - 2)

m(x) = (x + 3) · (x - 2)

Neither

f(x) = 3 · (x - 1) · (x + 2)

j(x) = (x - 2) · (x - 3)

To learn more on quadratic equations: https://brainly.com/question/17177510

#SPJ1

I need help solving this problem!

Answers

Answer: A

Step-by-step explanation:

The domain is the range of possible x that doesn't make y impossible to find, in this case, all real numbers work

The range is the range of possible y that doesn't make x impossible to find in the inverse function, in this case, all real numbers work

The answer is A.

As any number can be replaced in place of x for the function y, the domain of the function is All Real Numbers. Since any number can be inputted, the result will also vary accordingly. Hence, the range of the function is All Real  Numbers.

This is true for the listed function :

[tex]\boxed {y = \sqrt[3]{x-2} - 5}[/tex]

Write the ratio of 4 roses to 24 flowers

Answers

1:6

Initially we have 4:24 meaning 4 roses for 24 flowers. However, we can simplify this ration same as we do to fractions. If we divided both sides of the ration by 4, we get 1:6, or 1 rose for every 6 flowers.

Answer:

4:24 or also 1:6

Step-by-step explanation:

Do companies that provide mobile wifi hotspots see your history?

Answers

Yes, companies that provide mobile wifi hotspots can see your history.

What is a Wi-Fi hotspots?

A Wi-Fi hotspots can be defined as  the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.

For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .

Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.

Learn more about Wi-Fi hotspots here:https://brainly.com/question/7581402

https://brainly.com/question/17359340

#SPJ1

Find the value of z.
X
7
Y
3
Z

Z = √[?]

Answers

Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

help answer this please ​

Answers

Answer:

Step-by-step explanation:

2x + 5y = 8

      -5    -5

2x = 8 - 5y

divide both sides by 2

[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]

divide by 2 undoes the multiplication by 2

x = [tex]\frac{8- 5y}{2}[/tex]

divide 8 - 5y by 2

x = - [tex]\frac{5}{2}[/tex] y + 4

Stopyra Incorporated makes a single product—a cooling coil used in commercial refrigerators. The company has a standard cost system in which it applies overhead to this product based on the standard labor-hours allowed for the actual output of the period. Data concerning the most recent year appear below:
Budgeted variable manufacturing overhead $ 28,200
Budgeted fixed manufacturing overhead $ 89,280
Budgeted hours 12,000 labor-hours
Actual production (a) 16,000 units
Standard hours per unit (b) 0.60 labor-hours
Standard hours allowed for the actual production (a) × (b) 9,600 labor-hours
Actual variable manufacturing overhead $ 26,967
Actual fixed manufacturing overhead $ 74,280
Actual hours 8,900 labor-hours


The variable overhead rate variance is:
$6,528 U

$6,528 F

$6,052 U

$6,052 F

Answers

The variable overhead rate variance is: c. $6,052 U.

Variable overhead rate variance

First step is to calculate variable component of the predetermined overhead rate using this formula

Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours

Let plug in the formula

Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours

Variable component of the predetermined overhead rate=$2.35 per labor-hour

Second step is to calculate  variable overhead rate variance using this formula

Variable overhead rate variance=(AH×AR)-(AH×SR)

Let plug in the formula

Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)

Variable overhead rate variance= $ 26,967- $20,915

Variable overhead rate variance= $6,052 U (Unfavorable)

Therefore the variable overhead rate variance is: c. $6,052 U.

Learn more about  variable overhead rate variance here:https://brainly.com/question/27993032

https://brainly.com/question/17167100

#SPJ1

13
Company A has 800 employees, and it decides to grant each of the employees 50 share options as
part of its new rewards plan. The options are exercisable over 5 years and subject to a 3-year
service condition. The fair value of each option at the grant date is $16. The company estimates
that 80% of its employees will meet the service condition required for receiving the options.
Calculate the total share-based payment expense for Company A assuming that 80% of the
employees actually meet the service condition.

$512,000
$853,333
$341,333
$170,667

Answers

Option A. The total share expense that the company would share would be given as 512,000

What is meant by share expense?

These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.

How to solve for the share expense

The total number of the employees that are knwon to satistfy condition are given as

800 * 0.8

= 640

The options that are estmated that would be exercised

This is given as the employees * share option

= 640×50

=32000.

The total shae for the company would be gotten as

= 32000× $16

This gives us $512,000.

Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.

Read more on total shares here:

https://brainly.com/question/25788016

#SPJ1

add the two equations, 0.75x+1.5y=40 and −1.5x−1.5y=−60 , to find the value of x .

Answers

The value of x in the equation is 26.7

How to solve an equation?

0.75x + 1.5y = 40

−1.5x − 1.5y = −60

add both equation to eliminate y .

Therefore,

−1.5x + 0.75x = -0.75x

1.5y + (- 1.5y) = 0

40 + (-60) = -20

Hence,

-0.75x  = - 20

divide both sides by -0.75

-0.75x / -0/75 = - 20 / -0.75

x = - 20 / -0.75

x = 26.6666666667

x = 26.7

learn more on equation here:  brainly.com/question/7234676

#SPJ1

the width of a large butterfly is about 0.08. What is the width when it is written in scientific notation

Answers

Answer: 8 x 10^2

Step-by-step explanation:

scientific notation has to be greater than 1, less than 10

therefore:

0.08 = 8 x 10^2


Alok started a business investing Rs 90, 000. After three
months Prabir joined him with capital of Rs 1,20000
If at the end of 2 years, the total profit made
by them was
Rs 96,000 what will the difference
between Alok and Prabir's share in it?

Answers

The difference between Alok and Prabir share exists 8000.

What will the difference between Alok and Prabir share?

Given: Invested by Alok = Rs 90, 000

Invested by Prabir = Rs 1,20000

The time period of Alok = 3 months

The time period of Prabir = 2 years

They earn a profit = Rs 96,000.

Profit exists directly proportional to the product of the amount invested and the time period of investment.

8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21

= 5/7

5x + 7x = 96000

x = 8000

first = 40000

second = 48000

so the difference exists at 8000.

The difference between Alok and Prabir share exists 8000.

Therefore, the correct answer is 8000.

To learn more about the profit refer to; https://brainly.com/question/3883496

#SPJ9

What is the sum of ∞Σn=1 2(1/5)^n-1? s=1/5 s=2/5 s=5/3 s=5/2

Answers

The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

How to determine the sum of the notation?

The sum notation is given as:

∞Σn=1 2(1/5)^n-1

The above notation is a geometric sequence with the following parameters

Initial value, a = 2Common ratio, r = 1/5

The sum is then calculated as

S = a/(1 - r)

The equation becomes

S = 2/(1 - 1/5)

Evaluate the difference

S = 2/(4/5)

Express the equation as products

S = 2 * 5/4

Solve the expression

S= 5/2

Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

Read more about sum notation at

https://brainly.com/question/542712

#SPJ1

Answer:

S = 5/2

Thank me later

Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable , whose possible values are 0, 1, 3, 4, and 5.

Answers

For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:

P(X = 0) = 0.40.P(X = 1) = 0.04.

What is needed for a discrete random variable to represent a probability distribution?

The sum of all the probabilities must be of 1, hence:

P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.

Then, considering the table:

P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1

P(X = 0) + P(X = 1) + 0.56 = 1

P(X = 0) + P(X = 1) = 0.44.

Hence one possible example is:

P(X = 0) = 0.40.P(X = 1) = 0.04.

More can be learned about probability distributions at https://brainly.com/question/24802582

#SPJ1

pleaseee helpp
which of the following enequalities would produce the region indicated on the graph below

Answers

Answer: C

Step-by-step explanation:

The line [tex]y=x+2[/tex] is shaded below and is solid.

This eliminates all the options except for C.

Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}

Answers

Answer: 8.7 the mean is 20

Step-by-step explanation:

   

A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial position of the yo-yo at time t = 0 is x = 3.

Part A: Find the average value of v(t) on the interval open bracket 0 comma pi over 2 close bracket. (10 points)

Part B: What is the displacement of the yo-yo from time t = 0 to time t = π? (10 points)

Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)

Answers

Part A - The average value of v(t) over the interval  (0, π/2) is 6/π

Part B -  The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Part A: Find the average value of v(t) on the interval (0, π/2)

The average value of a function f(t) over the interval (a,b) is

[tex]f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx[/tex]

So, since  velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval  (0, π/2) is given by

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt[/tex]

Since v(t) = 3cost, we have

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}[/tex]

So, the average value of v(t) over the interval  (0, π/2) is 6/π

Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)

The total distance the yo-yo travels from time t = 0 to time t = π is given by

[tex]x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6[/tex]

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Learn more about average value of a function here:

https://brainly.com/question/15870615

#SPJ1

What is the best estimated volume of the figure?
can anyone solve this for me with a detailed explanation step by steps and reasoning so i can grasp concepts

Answers

The answer is 756 m³.

The formula to find volume is : length × width × height

To estimate, round each dimension to the nearest whole number.

⇒ 12.3 ≅ 12

⇒ 7.2 ≅ 7

⇒ 8.6 ≅ 9

Volume = 12 × 7 × 9

Volume = 84 × 9

Volume = 756 m³

Answer:

The ans to this question is 756 which is Option (B)

Step-by-step explanation:

Estimate volume = rounding every digit

= 12.3 = 12

= 7.2 = 7

= 8.6 = 9

= 12x7x9 = 756

Sodas cost $1.75 each. Write a direct
proportional equation using (s) for sodas and
(t) for total cost.

Answers

Answer:

t = 1.75(s)

Step-by-step explanation:

I gotchu

Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?

Answers

Answer:

1/5 of it

Step-by-step explanation:

5/5 represents all of her homework

5/5-4/5= 1/5

4/5 represents the homework she did before dinner

1/5 represents the homework left to do

20% i think bc if you divided 4/5 and multiply by 100 is says 80 so there is 20 more until 100

45.7 kilometers =
meters

Answers

Answer:

45.7 kilometers = 45,700 meters

Explanation:

Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.

Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).


Hope this helps!

Length conversion

To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.

Convert 45.7 kilometers to meters:

Knowing that 1000 m = 1 km.

               [tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]

45.7 km = 45,700 m

ヘ( ^o^)ノ\(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

https://brainly.com/question/15805924

Use the table values below to select the correct statement.

Answers

The true statement is (c) the function f(x) is an exponential function

How to determine the correct statement?

From the table, we can see that:

As x increases by 2.y does not increase with the same common difference

This means that the table represents an exponential function

The rate is then calculated as:

f(n) = f(1) * r^n-1

Using f(3), we have

102 = 17 * r^3-1

This gives

r^2 = 6

Take the square roots

r = 2.45

Hence, the true statement is (c) the function f(x) is an exponential function

Read more about exponential function at

https://brainly.com/question/11464095

#SPJ1

Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is rolling a sum less than 6. Which of the following shows the sample space of event A?

{(1, 1), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3)}
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 5), (2, 1), (2, 2), (2, 3), (3, 1), (3, 3), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (3, 3), (4, 1), (4, 2)}

Answers

the sample space is:

{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}

Which of the following shows the sample space of event A?

Event A is rolling a sum less than 6.

Let's define the possible elements in this experiment as:

(outcome of dice 1, outcome of dice 2)

The outcomes where the sum is less than 6 are:

dice 1    dice 2     sum

  1               1           2

  1               2           3

  1               3          4

  1               4          5

  2               1          3

  3              1           4

  4               1          5

  2              2          4

  3              2          5

  2              3           5

 

So there are 10 outcomes, then the sample space is:

{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}

If you want to learn more about sample spaces:

https://brainly.com/question/2117233

#SPJ1

Answer:

B) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}

Step-by-step explanation:

If the question said less than 6 meaning you have to find all possible solution that are 5 or lower.

However, if the problem said equal or less than 6 then you have to find all possible solution that are 6 or lower.

B option is only option that don't have sum of 6. Therefore, option B is correct.

Will mark brainliest

Answers

Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]

Recall the well-known power sum formulas,

[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]

Reducing our sum leads to

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]

As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to

[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]

Other Questions
What is the earth?(Original answer) Exercise 18: 3 1. The populations of a city increased from 4 million to 1.1 million. Write in digits the number by which the population increased.pls as fast as u can!!!!!!!!!!!!!!!! What is Initiating?A. Stopping work by being negative, interrupting, or talking about something elseB. Bringing up new ideasC. Asking constructive questionsD. Directing the discussionReset Selection Determine a solution to system of linear inequalities graphed and justify your answer. what is recitation say please If it is employing the rule of reason when considering an anti-trust case, the court? If the original Mandarin more closely matches the word Dao, why do most people refer to the religion as Taoism?a. The Wade-Giles system was older and more widely known.b. The Chinese government encouraged people to pronounce it Tao.c. Followers of Taoism have a superstition about using the word Dao.d.The regional accent of the followers has changed over time. What concept is most important in determining which good a person or nation will specialize in the prodution of? How does the area below the mean compare to the area above the mean in a normal distribution? What type of figurative language in "i can't talk to the walls anymore because they're yelling at me." James is sitting at his desk on the ground floor of an office building when the entire room starts shaking. which action is most appropriate in this situation? standing near a window running out of the building holding up a bookshelf preparing for aftershocks Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?6+3/n-86+n/3-86+3/n+86+n/3+8 chlorine + sulfur dioxide + water = hydrochloric acid + sulfuric acid An individual is seeking coverage for nursing home (custodial) care that does not require any previous period of hospitalization. Which program offers these specifications Which nursing actions would most likely help improve communication with clients and achieve a more effective helping relationship? the selling price of a mobile after discount is 10000.if the discount is 10% find the mp The tendency to immediately recall the first and last items in a list better than the middle items is referred to as the ________ effect. a) serial position b) misinformation c) next-in-line d) priming spacing number 7 please and don t care abt others lol In describing gender, instrumentality is traditionally associated with _____; while expressiveness is traditionally associated with _____. Solve the equation in the image (yr 8 maths, 50pts)