PLEASE HELP!!!
Solve.
-2x+3y-z=-2
3x + y = 4
-2y+2z=4
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.

PLEASE HELP!!! Solve.-2x+3y-z=-23x + Y = 4-2y+2z=4Enter Your Answer, In The Form (x, Y, Z), In The Boxes

Answers

Answer 1

Step-by-step explanation:

the second equation gives us right away

y = 4 - 3x

we can use that now in the 3rd equation :

-2(4 - 3x) + 2z = 4

-8 + 6x + 2z = 4

6x + 2z = 12

3x + z = 6

z = 6 - 3x

now we use both in the 1st equation :

-2x + 3(4 - 3x) - (6 - 3x) = -2

-2x + 12 - 9x - 6 + 3x = -2

-8x + 6 = -2

-8x = -8

x = 1

y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1

z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3

so,

(1, 1, 3)


Related Questions

como se puede usar la multiplicacion por 1 para encontrar fracciones equivalentes

Answers

Answer:

pamachino ala iscola iyo kapito binisimo bambena ilina

How do I write -2=y into slope intercept form?

Answers

Answer:

(0,-2)?

Step-by-step explanation:

Find the value of x.

Answers

Answer:that  a accute angle

Step-by-step explanation:

the length of a new rectangular playing field is yards longer than the width. if the perimeter of the rectangular playing field is ​yards, what are its​ dimensions?

Answers

The width is 53 yards and the length is 108 yards.

What is the perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter. There are several practical applications for calculating the perimeter.

To find the dimensions:

First, we'll turn the information we have into an equation, where x is our unknown dimension.For this problem, it would be preferable if x equaled width.Let's write the equation down:X is the width, 2x + 2 is the length, and we multiply both by two because the field has two sides. Because the perimeter is 322, it will all add up to 322.2 × x + 2(2x +2) = 322

Now, solve as follows:

2 × x + 2(2x + 2) = 3222x + 4x + 4 = 3226x + 4 = 3226x = 318x = 318 ÷ 6x = 53

The width measures 53 yards.

To calculate the length, multiply 53 by two and add two.

53 × 2 + 2 = 106 + 2 = 108 yards

Therefore, the width is 53 yards and the length is 108 yards.

Know more about perimeter here:

https://brainly.com/question/19819849

#SPJ4

The correct question is given below:
The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?

City workers are using a snowplow to clear a street. A tire on the snowplow is 3.2 ft in diameter and has to turn 35 times in traveling the length of the street.
How long is the street?
Use the value 3.14 for 1. Round your answer to the nearest tenth. Do not round any Intermediate steps.

Answers

351.7 ft is the length of the street

City workers are using a snowplow to clear a street. A tire on the snowplow is 3.2 ft in diameter and has to turn 35 times in traveling the length of the street.

The total distance of the street is the number of times the wheel turns multiplied by its circumference. Thus:

C = πD

L = nπD

L = 35 x 3.14 x 3.2

Use the value 3.14 for pi. Round your answer to the nearest tenth. Do not round any Intermediate steps

L = 351.7 ft

Hence 351.7 ft is the length of the street

learn more about of length here

https://brainly.com/question/2806054

#SPJ9

melissa drew a scale drawing of a city. a neighborhood park is 36 inches wide in the drawing. the actual park is 60 yards wide. what is the scale of the drawing?

Answers

The scale of the drawing by using proportion is 3 : 5.

According to the given question.

Melissa drew a scale drawing of a city.

The width of the park in the drawing is 36 inches.

And the actual width of the park is 60 yards.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Therefore, the scale of the drawing by using proportion

= 36iches/ 60 yards

= 3/5

= 3 : 5

Hence, the scale of the drawing by using proportion is 3 : 5.

Find out more information about scale here:

https://brainly.com/question/28060140

#SPJ4

Write an integer expression using absolute value symbols to represent the verbal expression.

the opposite of the absolute value of eight

Answers

The absolute value of the given integer(i.e. -7) is  7

Absolute value:

The absolute value (or modulus) | x | of a real number x is its non-negative value regardless of its sign.

A number's absolute value can be assumed as its distance from the origin along the real number line. Furthermore, the distance between two real numbers is the absolute value of their difference.

Let's assume the given integer=-7 and need to find the absolute value of the  given integer.

Then the absolute value of the given integer(i.e. -7) is  7

Therefore, The absolute value of the given integer(i.e. -7) is  7

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ9

What is limit as x approaches zero of f(f(x)) closest to?
a. DNE
b. 1
c. 3
d. 5

note: I thought the answer was does not exist, but it ended up being wrong, please help and explain the answer!

Answers

Using limits and numeric value, we have that lim x -> 0 f(f(x)) is closest to:

c. 3.

What is f(f(x))?

f(f(x)) is a composite function, hence:

For x = a, first we calculate the numeric value at x = a.Then we calculate the numeric value at x = f(a).

What is a limit?

A limit is the value that a function f(x) tends as x tends to a value. It there are no undetermined values, we can just verify the numeric value from the graph, but with undetermined values, there are multiple things to look at.

For this function, looking at the graph, we have that:

f(0) = 2, as when x = 0, f(x) = 2.Thus, lim x -> 0 f(f(x)) = lim x - > 2 f(x), because f(0) = 2.Both to the left of x = 2 and to the right of x = 3, from the graph, f(x) approaches 3, hence lim x - > 2 f(x) = 3.

This means that option c is the closest approximation for the limit of the function.

More can be learned about limits at https://brainly.com/question/26270080

#SPJ1

A metade dos objetos de uma caixa mais a terça parte desses objetos é igual a 25. Quantos objetos há na caixa? ​

Answers

Answer:

Explicação passo-a-passo:

Podemos atribuir a incógnita x ao número de objetos que há na caixa. Assim, teremos as seguintes relações:

Metade dos objetos da caixa = 1/2x

Terça parte dos objetos da caixa = 1/3x

Portanto, o número de objetos que há na caixa será dado resolvendo a equação:

1/2x + 1/3x = 25

3/6x + 2/6x = 25

5/6x = 25

x = 25/(5/6)

x = 25 . (6/5)

x = 150/5

x = 30

Novas perguntas de Matemática

1.Na portaria de um prédio chegaram, certo dia, 65 cartas. Desse total,1/5 foi entregue no 1°andar. Qual é o número de cartas distribuídas nos outros …

Faça um grafico da função f(x)= -x² +2x -1 Pfv!!

4. Em cada figura, AB é um diâmetro. Determine a medida x

O gráfico a seguir representa a função f(x)=a^x-1 em que a é positivo. Nessas condições, qual é o valor de A?

Maria começou a trabalhar numa loja de venda de sapato e receberá mensalmente um salário de r$ 1000 nós vamos comissão de 3

Um numero somado com

Brainly.com.br

Pesquise a resposta para qualquer pergunta...

ytzinhawww

ytzinhawww

há 5 minutos

Matemática

Ensino fundamental (básico)

1.Na portaria de um prédio chegaram, certo dia, 65 cartas. Desse total,1/5 foi entregue no 1°andar. Qual é o número de cartas distribuídas nos outros andares? (tem que fazer a conta)

a. 20

b. 35

C. 48

d. 52

2.foram entrevistados 420 candidatos a determinada vaga de um emprego. sabe-se que 5/7 desse número de candidatos foram rejeitados. Então, foram aceitos:

a. 300 candidatos

b. 210 candidatos

C. 380 candidatos

d. 120 candidatos

3.a figura está dividida em cinco partes iguais. a parte pintada representa:

⬜⬜⬜⬜

a. 10%

b. 12%

C. 20%

d. 25%

4.numa caixa 100 bolas, 45 são vermelhas, 20 são azuis, e o restantes são amarelas. em relação ao total a porcentagem de bolas amarelas é:

a. 55/100

b. 25/100

c. 45/100

d. 35/100

5.um dia tem 24 horas, uma hora tem 60 minutos e 1 minuto tem 60 segundos. a fração da hora que corresponde a 35 minutos é:

a. 7/4

b. 7/12

C.35/24

d. 60/35

6.dois terços da população de um município correspondem a 36000 habitantes. pode-se afirmar que esse município tem:

a) 18000 habitantes

b) 36000 habitantes

C) 48000 habitantes

d) 54000 habitantes

7.uma plantação foi feita de modo a ocupar 2/5

da terça parte da área de um sítio, como mostra a figura em relação à área total do sítio, a fraçao que representa a área ocupa por essa plantação é:

⬜⬜

⬜⬜

⬜⬜

⬜⬜

⬜⬜

bem por favor alguém me ajude preciso até amanhã pq é muito importante e se for me ajuda n esquece a conta pq a prof é bem exigente.tchau

The function f(x)=x^2 times the graph of g(x) is f(x) translated to the left 6 units and down 5 units. What is the function rule for g(x)?

Answers

The function rule for g(x) is (x₊6)² ₋ 5. According to the given data we apply the translations onto the graph and from the graph we determine the function of g(x).

Given, the function of f(x)  = x²

The base graph is moved up or down in the y-axis direction when a graph is vertically translated. Each point on a graph is moved k units up the graph to translate it vertically. Shifting the f (x) k units vertically will allow you to sketch the equation g (x) = f (x) + k.

The graph of g(x) is f(x) translated to 6 units left and down 5 unit.

Draw the translations onto the graph. In the given graph provided, the yellow curve indicates the function g(x).

therefore g(x) = (x₊6)² ₋ 5 is the function from the graph.

Learn more about Graphical problems here

brainly.com/question/4025726

#SPJ9

PLEASE HELP ILL MARK YOU BRAINLIST

Answers

the answer would be 2(4.75x)

EXPLANATION:
He is getting both his brother and sister truffles which the 2 represents.

The 1.75 is the cost per truffle
he gets them gift wrapped so you add the total of each costing truffle 1.75 + 3.00= 4.75

but doesn’t know the amount he will be getting which the X represents.

which gives you the equation of 2(4.75x)


place the following complex number in a two dimensional complex plane and find their absolute value "1+i)

Answers

The point (1,1) represents 1+i in the two dimensional complex plane. Absolute value of 1+i = [tex]\sqrt{2}[/tex].

Given the complex number, z = 1+i

The general form of a complex plane is x+iy, where x and y are real numbers.

We can place any complex number into a two-dimensional complex plane with two axes - X and Y.

For z = 1+i, x = 1 and y = 1. So the point (1,1) will represent z = 1+i in the two dimensional complex plane.

The absolute value of a complex number z = x+iy is given by ,

|z| = [tex]\sqrt{x^2+y^2}[/tex]

So for z = 1+i, |z| =  [tex]\sqrt{1^2+1^2}=\sqrt{2}[/tex]

Learn more about complex numbers at https://brainly.com/question/10662770

#SPJ4

i have four identical oranges. how many ways are there for me to divide these oranges into at most three groups? (by definition, a group must have at least one orange.)

Answers

Answer:

put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges

Step-by-step explanation:

Figure 2 shows 4 strips of paper formed from cutting ABCD. Figure 1 below shows a piece of rectangular paper ABCD where AB= (3x - 1) cm and BC= The total perimeter of the 4 strips is 170 cm. D C (b) Hence show that ABCD is a square. 2x+5 B 3x-1 Figure 1 (a) Form an algebraic equation in x and solve it. D 2x 326-1 Figure 2 C 2x75 = (2x + 5) cm. B​

Answers

(a) 2(3x-1) + 8(2x+5) = 170

Solve for x.
6x-2+16x+40=170
22x= 170+2-40
22x =132
x = 132/22 = 6

(b) Length AB = 3x-1 = 3(6)-1 = 17cm
Length BC = 2x+5 = 2(6)+5 = 17cm

Since length AB and BC are equal, Figure ABCD is a square of length 17cm.

I WILL GIVE BRAINIEST TO WHO ANSWERS RIGHT AND MORE POINTS

Answers

Answer:

x = 22 y = 113

Step-by-step explanation:

3x-15 = 2x+7

-2x         -2x

x-15 = 7

+15     +15

x = 22

180-51 = 129

y+16 = 129

-16       -16

y = 113

Answer:

x = 22

y = 113

Step-by-step explanation:

The angles marked as (2x+7) and (3x-15) are vertical angles, and therefore are equal to each other.

2x + 7 = 3x - 15 simplifying:

7 = x - 15

22 = x

Angles marked as (3x-15) and (y+16) form a linear pair and are therefore supplimetery. Now that we know the value of x, we can set up the following equation.

3(22) - 15 + y + 16 = 180 simplifying:

66 - 15 + y + 16 = 180

66 + y + 16 = 195

y = 113

Describe the solution to the system of equations graphed below.
3x+y=-6
9x+3y=-18
27
OA The system has the unique solution (3, 4)
OB. The system has infinitely many solutions of the form y=-3x-6 where x is any real number
OC. The system has no solution
OD. The system has the unique solution (3, 18)

Answers

Answer is B. Infinitely many solutions

Step by step

Solve the equation

Change the first equation to y intercept form

y = -3x -6

Substitute it into the 2nd equation for y and solve

9x + 3(-3x-6) = -18

Distribution multiply

9x -9x -18 = -18

Add 18 to both sides to isolate x

9x -9x -18 + 18 = -18 + 18

Combine like terms

0 = 0

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

Problem solved !!

Answer:

 A.

The system has infinitely many solutions of the form y = -3x - 6 where x is any real number.

Step-by-step explanation:

Write the slope intercept form of the equation for each line.

Answers

Answer: y=-4/5x-1.5

Step-by-step explanation: Both values are negative because your line is angled downwards from left to right and your y-intercept is below the x-intercept line.

Your 'b' or y-int is a little wonky, but I'm confident with what answer I'm handing to you.

68=3(6r-1)-7(1-3r) please help i need directions how not just an answer

Answers

Answer:

r=2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

68=3(6r−1)−7(1−3r)

68=(3)(6r)+(3)(−1)+(−7)(1)+(−7)(−3r)(Distribute)

68=18r+−3+−7+21r

68=(18r+21r)+(−3+−7)(Combine Like Terms)

68=39r+−10

68=39r−10

Step 2: Flip the equation.

39r−10=68

Step 3: Add 10 to both sides.

39r−10+10=68+10

39r=78

Step 4: Divide both sides by 39.

39r/39=78/39

r=2

g= 4a+4/ 5ca solve for A

Answers

The solution of the equation given as g = 4a +4/5 for a is a = 1/20(5g - 4)

How to solve for in the equation?

The equation is given as

g = 4a +4/5

Multiply through the equation by 5

So, we have

5 * (g = 4a +4/5)

Evaluate the products

So, we have

5g = 20a + 4

Subtract 4 from both sides of the equation

So, we have

20a = 5g - 4

Divide through the equation by 20

So, we have

a = 1/20(5g - 4)

Hence, the solution of the equation given as g = 4a +4/5 for a is a = 1/20(5g - 4)

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

What’s the domain and range?

Answers

Answer:

Domain: x > -4

Range: y > -1

Step-by-step explanation:

Domain is the points on the x axis that could be vaild for that line.

Range is the points on the y axis that could be valid for that line.

The domain is: -4 < x < ∞
The range is: -4 < y < ∞

To find the domain, we need to look at the graph from a left-to-right standpoint (look at the x-axis). When doing so, the furthest point to the left we see is -4. Given that value, we put that as the first value. Then, we can put x since we’re looking at the x-axis. That would leave us with:

-4 < x < ?

Since there is an arrow on the farthest right side, we would put an infinity sign because it goes on forever. The same process is applied to the y-axis, and when doing so, we will get the same answer but with y.

◄) Which lists contain only irrational
numbers? Select all that apply.
-11.8, -7.3, -9.7, -3, 61.4
√20
I
25
100
50,
21 3 1 2 1
22' 11' 9'
5' 17
I
35, 65 70
I
-
81,√36
I
144,
2/2,5/5,3/3, 6√6,7√7
(

Answers

Answer:

the 2 nd and 5 th box contain irrational number

Step-by-step explanation:

1 St and 3 Rd are clearly rational and 4 th can be converted into rational like root 25 is 5.

FIRST PERSON GETS BRAINLIEST

A triangle on a coordinate plane is translated according to the rule T–8, 4(x, y). Which is another way to write this rule?

(x, y) → (x + 4, y – 8)

(x, y) → (x – 4, y – 8)

(x, y) → (x – 8, y + 4)

(x, y) → (x + 8, y – 4)

Answers

Another way to write this rule is (x, y) = (x - 8, y + 4)

Which is another way to write this rule?

The translation rule is given as:

T–8, 4(x, y).

The above means that

x = x - 8

y = y + 4

Express as a transformation rule

So, we have

(x - 8, y + 4)

Rewrite as:

(x, y) = (x - 8, y + 4)

Hence, another way to write this rule is (x, y) = (x - 8, y + 4)

Read more about translation at:

https://brainly.com/question/26238840

#SPJ1

14 points :) please explain thank you so much!

Answers

The domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

What is the domain of a function?

The domain of the function is the set of input values of the graph

What is the range of a function?

The range of a function is the set of output values of the graph.

How to determine the domain and the range?

The graph represents the given parameters

On the graph, we have the following endpoints

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

The domain

The definition of the domain implies that the domain of a function is the set of x values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the maximum

Closed circle at (-2, -1)

Open circle at (-5, -2)

Remove the y coordinates

So, we have

Closed circle at (-2)

Open circle at (-5)

Combine the x values

-2 ≤ x < -5

The range

The definition of the range implies that the range of a function is the set of y values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the smaller larger y value of the endpoints)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the x coordinates

So, we have

Open circle at (-2)

Maximum = (1)

Combine the y values

-2 < y < 1

Hence, the domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

`y=2x^{2}+12x+20` find the vertex

Answers

Answer: (-3,2)

Step-by-step explanation:

Answer:

(-3, 2)

Step-by-step explanation:

There are two methods on finding the vertex. The one I will be using is the faster version.

y=2x^{2}+12x+20

a=2   b=12   c=20

First use the formula -b/2a.

-(12)/2(2)=

=-12/4=-3

-3 is the x-coordinate.

Plug in -3 into the equation for x.

y=2(-3)^{2}+12(-3)+20

y=2(9)+12(-3)+20

y=18-36+20

y=2

The y-coordinate is 2

Use (x, y) for the vertex.

x=-3

y=2

The vertex is (-3, 2)

Hope this helps!

Please mark as brainliest if correct!

please find x to this. 5/9x -11 = -51

Answers

5/9x -11 = -51

5/9x = 11 - 51

5/9x = -40

5x = -360

x = -72

Find the distance between the two points shown on the graph below, located at (1, 2) and (3, 1).

Answers

The distance between the two points as depicted on the graph is:

√5.

Given, the points are:

(1,2) = (x₁,y₁) and

(3,1) = (x₂,y₂)

We know that distance between two points is:

d = √(x₂-x₁)²+(y₂-y₁)²

d = √(3-1)²+(1-2)²

d = √(2)²+(-1)²

d = √4+1

d = √5

Hence we get the distance between two given points as √5

Learn more about Coordinate geometry here:

https://brainly.com/question/7243416

#SPJ9

Turn these into ratios, what is the simplest form?

Answers

Answer:

1. [tex] \frac{39}{59} = 39:59[/tex]

2. [tex]\frac{52}{120} = 13:30[/tex]

The above should be what you're looking for

if a line passed through (0,0),(1,8),(3,24) and (x,44) what is x?

Answers

Answer: x=5.5

Step-by-step explanation:

First you need to find the slope using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. Thankfully, we have (0, 0) and (1, 8) as points, which makes it easy to find that the slope is 8.

Once we have the slope, we divide 44 by 8 to get 5.5

Please help my I ready is due today !!!

Answers

Answer:

calculate the number of terms of the series 5;8;11;...173

If 75% of the employees in a company are female and 5% of those female employees are over 6 feet tall what percentage of the company’s employees are both female and over 6 feet tall

Answers

The percentage of the company’s employees are both female and over 6 feet tall is 3.75%

Let the total number of employees in the given company be x. So, the number of female employees in the company are : 75% × x

Number of female employees in company = 0.75x

Now, calculating number of female employees that over 6 feet tall = 0.75x × 5%

The number of female employees that over 6 feet tall = 0.0375x

Percentage of the company’s employees are both female and over 6 feet tall = percentage of female and tall employees ÷ total number of employees × 100

Percentage of the company’s employees are both female and over 6 feet tall = (0.0375x÷x)×100

Percentage of the company’s employees are both female and over 6 feet tall = 3.75%

Therefore, the percentage of the company’s employees are both female and over 6 feet tall is 3.75%

Learn more about percentage -

https://brainly.com/question/24304697

#SPJ9

Other Questions
most purchase agreements are contingent on which two items? appraised value property description clear title title insurance cost of inputs increases number of sellers decreases these changes would most likely have which impact on the market? a) supply would increase b) supply would decrease c) demand would increase d) demand would decrease what is the cost to drive in san fransisco to la (405 miles) if the cost of gasoline is $3.85/gal and the car gets 24 mil/gal? lower-level managers' decision-making authority can be linked to the outcomes of those decisions through . Brain plasticity refers to which of the following?O The ability of brain tissue to take on new functionsO Healthy human brain tissueO A wide variety of functions performed by the human brainO The ability of the brain to transfer information from one hemisphere to the otherO How a brain gets larger as a child grows Which organelle accurately completes the chart PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT how does indigenous ways of knowing different from canadian ways of knowing A flood is a type of natural disaster that can be caused due to heavy and continuous rainfall at a place for a long time. change passive verb PLEASE HELP.100 pointsBoyle's law states that the pressure of a gas tends to increase as the volume of the container holding the gas decreases.Which explains why this is a law rather than a theory?A.It is a statement of fact.B.It explains how the pressure of gases changes.C.It has been revised and replaced over time.D.It has changed due to advances in technology. Given , find the average rate of change of f(x)=[tex]f(x)=\frac{1}{x+5}[/tex] on the interval[1,1+h]. Your answer will be an expression involving h.Pls halp can someone please anwser (5z+y)/7 (the number values of z and y are in the picture) which organization provides published guidelines that support the core principles of patient-centered quality care decide whether the following statement is true or false, and then explain why: "in an organism whose genome has been sequenced, identifying the mutant gene responsible for an interesting phenotype is as easy for mutations induced by chemical mutagenesis as it is for those generated by insertional mutagenesis" psycharvixthe limits of religious tolerance: individual and contextual determinants of who can violate religious norms. Which statement best describes why a chemical change is different from a physical change?A chemical change is used to identify characteristics of a substance, and a physical change identifies the behavior of a substance when in a reaction.A chemical change results in a new substance being formed, whereas a physical change will result in a different state of matter.A chemical change results in a different state of matter, and a physical change results in a new substance being formed.A chemical change is used by scientists to create new substances, and a physical change happens naturally. which matter is considered when calculating a country's balance of payments? multiple choice military expenditures domestic inflation rates foreign inflation rates state unemployment Jenna bought a new car for $37,000$37,000. She paid a 10%10% down payment and financed the remaining balance for 7272 months with an APR of 6.5%6.5%. Assuming she makes monthly payments, determine the total interest Jenna pays over the life of the loan. Round your answer to the nearest cent, if necessary.Formulas Read the following passage from Anne of Green Gables by Lucy Maud Montgomery. Answer the question that follows the text."Oh, you can talk as much as you like. I don't mind.""Oh, I'm so glad. I know you and I are going to get along together fine. It's such a relief to talk when one wants to and not be told that children should be seen and not heard. I've had that said to me a million times if I have once. And people laugh at me because I use big words. But if you have big ideas you have to use big words to express them, haven't you?""Well now, that seems reasonable," said Matthew."Mrs. Spencer said that my tongue must be hung in the middle. But it isn'tit's firmly fastened at one end. Mrs. Spencer said your place was named Green Gables. I asked her all about it. And she said there were trees all around it. I was gladder than ever. I just love trees. And there weren't any at all about the asylum, only a few poor weeny-teeny things out in front with little whitewashed cagey things about them. They just looked like orphans themselves, those trees did. It used to make me want to cry to look at them. I used to say to them, 'Oh, you POOR little things! If you were out in a great big woods with other trees all around you and little mosses and Junebells growing over your roots and a brook not far away and birds singing in you branches, you could grow, couldn't you? But you can't where you are. I know just exactly how you feel, little trees.' I felt sorry to leave them behind this morning. You do get so attached to things like that, don't you? Is there a brook anywhere near Green Gables? I forgot to ask Mrs. Spencer that.""Well now, yes, there's one right below the house.""Fancy. It's always been one of my dreams to live near a brook. I never expected I would, though. Dreams don't often come true, do they? Wouldn't it be nice if they did? But just now I feel pretty nearly perfectly happy. I can't feel exactly perfectly happy becausewell, what color would you call this?"She twitched one of her long glossy braids over her thin shoulder and held it up before Matthew's eyes. Matthew was not used to deciding on the tints of ladies' tresses, but in this case there couldn't be much doubt."It's red, ain't it?" he said.The girl let the braid drop back with a sigh that seemed to come from her very toes and to exhale forth all the sorrows of the ages."Yes, it's red," she said resignedly. "Now you see why I can't be perfectly happy. Nobody could who has red hair. I don't mind the other things so muchthe freckles and the green eyes and my skinniness. I can imagine them away. I can imagine that I have a beautiful rose-leaf complexion and lovely starry violet eyes. But I CANNOT imagine that red hair away. I do my best. I think to myself, 'Now my hair is a glorious black, black as the raven's wing.' But all the time I KNOW it is just plain red and it breaks my heart. It will be my lifelong sorrow. I read of a girl once in a novel who had a lifelong sorrow but it wasn't red hair. Her hair was pure gold rippling back from her alabaster brow. What is an alabaster brow? I never could find out. Can you tell me?""Well now, I'm afraid I can't," said Matthew, who was getting a little dizzy. He felt as he had once felt in his rash youth when another boy had enticed him on the merry-go-round at a picnic."Well, whatever it was it must have been something nice because she was divinely beautiful. Have you ever imagined what it must feel like to be divinely beautiful?""Well now, no, I haven't," confessed Matthew ingenuously."I have, often. Which would you rather be if you had the choice-divinely beautiful or dazzlingly clever or angelically good?""Well now, I-I don't know exactly.""Neither do I. I can never decide. But it doesn't make much real difference for it isn't likely I'll ever be either."In a minimum of one paragraph, explain what you learn about these characters from this interaction. Use details from the passage to support your response. Find the direction of this vector.80.0B-18.6 m0 = [?]Hint: Remember, 0 is the direction of thevector and is measured from the +x-axis.