Two terms of an arithmetic sequence are a7 = 32 and a19 =140. . Find n such that Sn = 511

Answers

Answer 1

In an arithmetic sequence, consecutive terms differ by a fixed number d :

[tex]a_8=a_7+d[/tex]

[tex]a_9=a_8+d=a_7+2d[/tex]

[tex]a_{10}=a_9+d=a_7+3d[/tex]

and so on up to

[tex]a_{19}=a_7+12d[/tex]

Solve for d :

[tex]140=32+12d\implies12d=108\implies d=9[/tex]

Work backwards to find the first term in the sequence, and hence the n-th term:

[tex]a_6=a_7-d[/tex]

[tex]a_5=a_6-d=a_7-2d[/tex]

and so on down to

[tex]a_1=a_7-6d[/tex]

So the first term is

[tex]a_1=32-6\cdot9=-22[/tex]

which means the n-th term is

[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]

[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:

[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]

Distribute the summation and recall the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

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

[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]

[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]

[tex]\implies1022=9n^2-53n[/tex]

[tex]\implies9n^2-53n-1022=0[/tex]

[tex]\implies(n-14)(9n+73)=0[/tex]

[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]

n must be a positive integer, so we the sum is obtained from the first n = 14 terms.


Related Questions

PLEASE I REALLY NEED HELP What differences are there on the graph of f(x)=2x to the graph of h(x)=2x-3?

Answers

Answer:

The graph if h(x) =2x-3 will have the same slope, but placed lower on the graph, because it's y intercept is -3, while the y-int of f(x) is 0, which is higher up on the y axis

A rectangle with an area of x2 – 4x – 12 square units is represented by the model. What side lengths should be used to model the rectangle? (x + 2) and (x – 6) (x + 6) and (x – 2) (x + 2) and (x – 10) (x + 10) and (x – 2)

Answers

Answer: (x+2) and (x-6) represents the side lengths.

Step-by-step explanation:

The area of the rectangle is [tex]x^{2} -4x -12[/tex] so in this case to find the side lengths we need to factor out the area.

To factor [tex]x^{2} -4x-12[/tex]  We need to find two numbers that if we multiply together we will have -12 and if we add those two number we will get -4.

-6 and 2 works out  

Because -6 * 2 = -12 and -6 +2 = -4

Now we will rewrite the area as

[tex]x^{2}[/tex] +2x - 6x -12   Group them  

([tex]x^{2}[/tex] +2x) (-6x -12)  factor them

x (x +2)  -6(x+2)  factor out x+2

(x+2)(x-6)  Done!

Answer: The correct answer is A (x+2)(x-6) on Edg 2020;)

Do 26 and if u want to do 27 too I’ll give Brainlynest

Answers

Answer:

26) translation: (x - 4, y + 3)

27) see down below

Step-by-step explanation:

26) Its a translation since the shape isn't reflected nor rotated. To find the translation, you can see that the shape would move 4 to the left (- 4), and up 3 ( + 3), which gives you (x - 4, y + 3) (x determines left/right and y determines up/down).

27)

<1 = 135

<2 = 45

<3 = 45

<4 = x = 20

<5 = 135

<6 = 45

<8 = 135

You can do one or both if u do both I’ll give Brainlynest

Answers

Answer:

18) a. X

19) d. 69°

Step-by-step explanation:

18) A reflection is a transformation where an image is flipped over a line. So V will still be in the same place, it will just be flipped over line B. The only answer that makes sense in X.

19) All the angles in the picture are vertical angles. Vertical angles are angles that are across from each other when two lines cross and they are always equal.

The angle opposite the angle that is 78° is also 78°.

The angle opposite the angle that is 33° is also 33°.

The three angles form a straight line so:

78° + 33° + x = 180°

111° + x = 180°

x = 69°

Since the angle is a vertical angle and is opposite angle a, angle a will also be 69°.

Hope this helps. :)

Please answer it now in two minutes

Answers

Answer:

Triangle E, F, G and Triangle T, U, V.

Step-by-step explanation:

They both are congruent because have the same shape, same size, and they both mirror each other.

Answer:

Triangle EFG and triangle TVU

Step-by-step explanation:

You must use congruent segments and keep track of the corresponding sides and vertices.

Triangle EFG and triangle TVU

what are the points of intersection of -x^2+9x-3 and y=3x

Answers

Answer:

Easiest and fastest way is to graph both equations into a graphing calc and trace the graph to where they intersect.

Alternatively, you can use substitution to solve for your answer.

Step-by-step explanation:

1) Point M divides line segment AB, in the direction from A to B. in a ratio of 4 to 9. What value on the number line
would indicate the location of point M?​

Answers

Answer:

Point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].

Step-by-step explanation:

Two points A and B have been given on a number line.

Point A is at -3 and point B at 7.

Distance between these points AB = 7 - (-3)

                                                           = 7 + 3

                                                           = 10 units

Another point M divides the given segment AB in the ratio of 4 : 9.

Therefore, length of segment AM will be = [tex]\frac{4\times 10}{(4+9)}[/tex]

                                                                    = [tex]\frac{40}{13}[/tex]

                                                                    = [tex]3\frac{1}{13}[/tex] units

Now the position of point M will be at [tex](-3+3\frac{1}{13})[/tex] = [tex]\frac{1}{13}[/tex]

Therefore, point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].

Consider triangle ABC. Triangle A B C. Angle C is 80 degrees and angles B and A are y degrees. What is the value of y in the triangle? Angle y = °

Answers

Answer:

y is equal to 50 degrees.

Step-by-step explanation:

The sum of the angles of a triangle is always 180 degrees.  To find what y is, subtract 80 from 180 and divide the difference by 2.  This will give you 50 degrees.

Answer:

y= 50°

Step-by-step explanation:

∠A =∠B = y. So, ΔABC is an isosceles triangle.

Sum of angles of triangle = 180

∠A + ∠B + ∠C = 180

y + y + 80 = 180   {add like terms}

2y + 80 = 180  {Subtract 80 from both sides}

2y + 80 - 80 = 180 - 80

2y = 100   {divide both sides by 2}

2y/2 = 100/2

y= 50°

explain the differences between an equation and an equality. how do those differences affect solutions.

Answers

Answer:. An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other. 2. An equation shows the equality of two variables while an inequality shows the inequality of two variables.

Step-by-step explanation:

What value of n makes the equation true?
-1/5n + 7=2
n=​

Answers

Answer:

n = 25

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and is:

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

~

First, subtract 7 from both sides:

(-1/5)n + 7 (-7) = 2 (-7)

(-1/5)n = 2 - 7

(-1/5)n = -5

Next, multiply -5 from both sides:

(-1/5)(-5)n = (-5)(-5)

n = -5 * -5

n = 25

25 is your answer for n.

~

Answer: n = 25

Step-by-step explanation: In this equation, our first step is to isolate the n term by subtracting 7 from both sides.

On the left, +7 -7 cancels and we're left with -1/5n.

On the right, 2 - 7 simplifies to -5.

So we have -1/5n = -5.

In order to get n by itself, since it's being multiplied by a fraction,

we multiply both sides of the equation by the reciprocal of that fraction.

The reciprocal of -1/5 is -5/1.

So we multiply both sides of the equation by -5/1.

So we have (-5/1)(-1/5n) = -5(-5/1).

On the left, our 1's cancel and our 1's cancel.

Also, remember that a negative times a negative is a positive.

So on the left we are left with n.

On the right, -5(-5/1) is 25.

So n = 25.

The ant repeats the two steps 7 times going around the polygon until it reaches its starting position .the ant makes one complete revolution (360 degree) to draw this regular 7 sided polygon. The value of A correct to 1 decimal place is ____________

Answers

Answer:

(C)51.4 degrees

Step-by-step explanation:

The sum of the exterior angle of a polygon is 360 degrees. (one complete revolution).

Given a regular polygon, the sum of each exterior angle is calculated using the formula:

[tex]\dfrac{360^\circ}{n}[/tex] where n is the number of sides.

The regular polygon shown made by the ant has 7 sides.

Therefore:

Each exterior angle [tex]=\dfrac{360^\circ}{7}=51.43^\circ[/tex]

Therefore:

The value of A correct to 1 decimal place is 51.4 degrees.

The correct option is C.

Answer:

The correct value of A to 1 decimal place is [tex]51.4^o[/tex].

Step-by-step explanation:

Given information:

The ant repeats the two steps 7 times going around the polygon

The sum of the exterior angle of polygon is [tex]360^o[/tex]

The formula for the exterior angle is

[tex]= 360/n[/tex]

Here,

[tex]n=7[/tex]

Hence, the Value of A will be

[tex]A=360/7\\A=51.4^o[/tex]

The correct value of A to 1 decimal place is [tex]51.4^o[/tex].

For more information visit:

https://brainly.com/question/21212890

An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?

Answers

Answer:

hope it will help uh.....

Which equation has no solution?

1. 4(x+3)+2x=6(x+2)
2. 5+2(3+2x)=x+3(x+1)
3. 5(x+3)+x=4(x+3)+3
4. 4+6(2+x)=2(3x+8)

Answers

Answer:

Number 3 does not have a solution

Step-by-step explanation:

Does anyone know the answer to the table below?

Answers

Hey there! :)

Answer:

16 minutes.

Step-by-step explanation:

Create an equation in the form y = mx + b to solve this problem. Begin by solving for the rate of change of the table using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in values from the table into the equation:

[tex]m = \frac{64 - 40}{9 - 5}[/tex]

Simplify:

[tex]m = \frac{24}{4}[/tex]

m = 6.

Plug in the slope and a point from the table into the equation

y = mx + b

40 = 6(5) + b

40 = 30 + b

40 - 30 = b

b = 10.

Rewrite the equation:

y = 6x + 10

To solve for how long it took her to ride 1 km, plug 1 into the equation:

y = 6(1) + 10

y = 6 + 10

y = 16 minutes.

4x - 1
2.
= x + 7
Can someone help please?

Answers

Answer:

6[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

4x-12 = x+7

4x-12+12 = x+7+12

4x = x+19

4x-x = x+19-x

3x=19

x = 6[tex]\frac{1}{3}[/tex]

And if we substitute the value of x into the equation 4x-12 = x+7,

we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.

Hope this helps :)

Answer:19/3 = [tex]6\frac{1}{3}[/tex]Step-by-step explanation:[tex]4x -12= x+7\\Collect-Like-Terms\\4x-x =7+12\\3x=19\\Divide -Both-Sides-Of-The-Equation-By ; 3\\\frac{3x}{3} =\frac{19}{3} \\\\x = \frac{19}{3}\\ \\x = 6.3\\[/tex]

HELP ME PLEASE ~ Thanks :)

Answers

Answer:

A

Step-by-step explanation:

99/479

formula: girls in action divided by everyone

Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?

Answers

Answer:

  3 1/3 hours

Step-by-step explanation:

In 2 hours, the first guy did 2/6 = 1/3 of the job. Meanwhile, the new guy did 2/8 = 1/4 of the job. When the first guy left, the remaining amount of the job was ...

  1 - 1/3 - 1/4 = 12/12 -4/12 -3/12 = 5/12 . . . . . fraction of job remaining

So, completion of the remaining 5/12 of the job will take the new guy ...

  (5/12)(8 hours) = 10/3 hours = 3 1/3 hours


The temperature each hour in Elma, Texas on October 1 is modelled by the equation
t(h) = 10 cos(15h - 10)° + 30 where his hour of the day with 0 meaning midnight, and t is the
temperature in degrees Celsius. How hot did it get in Elma on October 1?

Answers

Answer:

[tex]39.8^{\circ} C[/tex]

Step-by-step explanation:

We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation

[tex]t(h)=10cos(15h-10)^{\circ}+30[/tex]

Where h=Hour of the day with 0 meaning midnight

t=Temperature in degree Celsius

We have to find the temperature on October 1.

Substitute h=0

[tex]t(0)=10cos(15(0)-10)+30[/tex]

[tex]t(0)=10cos(-10)+30[/tex]

[tex]t(0)=39.8^{\circ} C[/tex]

Hence, the temperature in Elma on October 1=[tex]39.8^{\circ} C[/tex]

A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?

Answers

Answer:

children take 3 pieces of candy are 6

Step-by-step explanation:

x+y=19-1          x+y=18

3x+5y=85-7    3x+5y=78

eliminate x by multiplying the first equation by 3:

3x+3y=54

3x+5y=85   subtract

(3x+3y)-(3x+6y)=54-78

3x-3y-3x-5y=-24

-2y=-24         y=-24/-2=12

y=12 , substitute for y:

x+y=18

x=18-12

x=6

check: 3x+5y=78

3(6)+5(12)=78

18+60=78 correct

I'm kind of unsure of my answer, please help me. I appreciate your answers.

Find two consecutive integers whose sum is 113. Which of the following equations could be used to solve the problem?

choices:
2 x + 1 = 113
[tex]x^{2}[/tex] + 1= 113
2 x = 113
2 x + 2 = 113

Answers

Answer:

We can call the numbers x and x + 1. Then we can write:

x + x + 1 = 113 which simplifies to 2x + 1 = 113.

Answer:

Hey there!

The correct answer would be x+x+1=113, or 2x+1=113.

Let the smaller number be x, then the larger number would be x+1

Thus, the sum of x and x+1 would be 2x+1.

We have that 2x+1=113.

Now, this is just a simple linear equation we have to solve.

Start by subtracting 1 to get 2x=112

Then, divide by 2 to get x=56

Since x=56, x+1 would be 57.

Thus, you would have the two numbers be 56 and 57, and use 2x+1 to solve.

Hope this helps :)

Please answer! I will mark brainliest for best answer :)

Answers

Answer:

5

Step-by-step explanation:

Number of players injured in a game count the other side

Linear Equations HELP ASAP

Answers

Answer: D) y = -1/4x + 6

Step-by-step explanation:

First turn the equation into slope-intercept form: y = 4x + 6

For a line to be perpendicular to another line, it's slope must be the opposite reciprocal of the other perpendicular line.  Thus, the slope of the perpendicular line is -1/4.  As the y-intercept of the line is (0,6), the lines must intersect as (0,6).  Thus, the other line must also have a y-intercept of 6.  Thus, the answer is D.

Hope this helps <3

Triangle X Y Z is shown. If m∠X = 34° and m∠Z = 26°, what is m∠Y?

Answers

Answer:

given, triangle XYZ in which m of angle X=34°

angle Z= 26°

now,angle Y =?

we have,

AngleX + angle Y+ angle Z = 180°

or, 34°+angle Y +26°=180°

or, angle Y= 180°-60°

therefore, angle Y =120°.

hope it helped..

Answer:

Triangle X Y Z is shown.

If m∠X = 34° and m∠Z = 26°, what is m∠Y?

Answer:

m∠Y = 120°

Step-by-step explanation:

I just took the test and got 100% on Edge2021

2a + 5a x 4a - a simplify

Answers

Answer:

20a² + a

= a(20a + 1)

Step-by-step explanation:

2a + 5a × 4a - a

= 2a + 20a² - a

= 20a² + a

find the 7th term of the geometric progression which begins with -6250,1250,-250

Answers

Answer:

a₇ = - 0.4

Step-by-step explanation:

The n th term of a geometric progression is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 6250 and r = [tex]\frac{1250}{-6250}[/tex] = - [tex]\frac{1}{5}[/tex] , thus

a₇ = - 6250 × [tex](-\frac{1}{5}) ^{6}[/tex]

    = - 6250 × [tex]\frac{1}{15625}[/tex] = - [tex]\frac{6250}{15625}[/tex] = - 0.4

What is the range of the function shown on the graph above?

Answers

Answer:

A.

Step-by-step explanation:

Since range is y-axis based, we are looking at the y-values. We see that the endpoints of the graphed segment are closed points, so they are included in the range. That eliminates B (exludes values) and C (Not infinity, it's a segment, not a line). Choice A is the best answer because when you identify the y-values, you get -8 to -3 included.

Plz write it for me how u got it ❤️On paper then send it to me

Answers

Answer:

See below in bold.

Step-by-step explanation:

1. x^2 - 13x - 30

We need 2 numbers whose product is -30 and whose sum = -13.

They are  -15 and + 2:

Answer is (x - 15)(x + 2).

2.   2x^2 + 4x - 126

First we can take 2 out to give:

2(x^2 + 2x - 63)

Now we need 2 numbers whose product is - 63 and sum = +2.

These are +9 and - 7 so

Answer is  2(x - 7)(x + 9).

3. -30x^3 + 3x^2 + 9x

First we can take out -3x to give

-3x(10x^2 - x - 3)

Now we want  2 numbers whose product is 10*-3  = -30 and whose sum is -1. They are  -6 and +5 so we write the above as:

-3x(10x^2 + 5x - 6x - 3)

Now we factor the parentheses by grouping:

= -3x( 5x(2x + 1) - 3(2x + 1)

= -3x(2x + 1)(5x - 3)  Answer.

The answer to the second part is 12x^2 - 13x - 21.

Part 3

1, 18.

2. 6.

3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2

=  5*(67) - 2(72) - 48

= 143.

4.  (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)

= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9

=  8m^2 - 4m - 5

A = 8, B = 4 and C = 5.

Find the probability that a student earns a grade D or F

Answers

Answer: P = 1/7

Explanation:
There 35 students total and there are 3 students with grade D and 2 students with Grade F

3/35 + 2/35 = 5/35 = 1/7

Answer:

P=.14 or 1/7

Step-by-step explanation:

P(d)=3/35

P(f)=2/35

P( D or F) = 3/35 + 2/35=

1/7 or .14

Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?

Answers

Complete Question:

To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².

Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?

Answer:

To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more

Step-by-step explanation:

Mass of burlap sacks that Maryann collects = 6 kg

Area density of burlap = 0.4 kg/m²

Area Density = Mass / Area........(1)

The Area of bulletin board that can be made with the 6 kg of burlap sand can be calculated by using equation (1)

0.4 = 6 / Area

Area = 6/0.4

Area of bulletin board that can be made from 6 kg= 15 m² of bulletin board  

The area of bulletin board that Maryann made for herself = 2 * 3 = 6m²

To make similar bulletin boards for her four friends, the total area of bulletin board made for her 4 friends = 6 * 4 = 24m²

To calculate the mass of burlap required to make a 24m² bulletin board, use equation (1)

0.4 = Mass / 24

Mass = 0.4 * 24

Mass = 9.6 kg

The mass of burlap used to make Maryann's bulletin board alone:

0.4 = Mass/6

Mass = 2.4 kg

Out of the 6kg that she got, she has used 2.4 kg for herself

The remaining mass of burlap = 6 - 2.4 = 3.6 kg

Therefore, to complete the bulletin board for her friend, she should collect (9.6 - 3.6) = 6 kg of bulletin more

2.2 units to the right of 0 horizontal number line

Answers

Answer:

2.2

Step-by-step explanation:

2.2 units to the right of zero indicates that the integer is positive on a horizontal number line.

0 + 2.2 = 2.2

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Read the excerpt from "Do not go gentle into that goodnight."Though wise men at their end know dark is right,Because their words had forked no lightning theyDo not go gentle into that good night.Good men, the last wave by, crying how brightTheir frail deeds might have danced in a green bay,Rage, rage against the dying of the lightWild men who caught and sang the sun in flight,And learn, too late, they grieved it on its way,Do not go gentle into that good night.Grave men, near death, who see with blinding sightBlind eyes could blaze like meteors and be gay,Rage, rage against the dying of the light.Which statement best describes the effect of therepetition of "men" preceded by an adjective?It reinforces the idea that all people, not just thespeaker's father, should fight against death.It emphasizes that all men, no matter what theirlives have been like, should accept death when itcomes.It supports the speaker's idea of an eternal life afterdeath for people of all walks of life.It highlights the speaker's grief at being unable tocome to his dying father's bedside. You may argue that it is impossible for two contradictory interpretations to be correct at the same time. Or you might point out that interpretations can be correct in many different ways. This graph compares the cost of room and board at educational institutions in Texas. This graph helps explain why -public community colleges are considered to be affordable alternatives to private community colleges. -students in Texas have become increasingly drawn to technical schools over community colleges. -many students might choose an alternative living situation overpaying room and board at a four-year institution. -some Texas students have opted to delay attaining a degree in higher education for several years. Evaluate geometric series sigma1^20 4(8/9)^n-1 Which products are formed when aluminum is added to a silver chlorine solution? Bee stings release methanoic acid which attacks the nerves in the skin. They can beneutralized by applying a cream that containsa) ammoniab) vitamin Cc) sulphur dioxided) acetic acid (vinegar) Compltez avec l'adjectif tout, toute, tous, toutes: x8=4 a) ________________ mes voisines viennent aujourd'hui. b) ________________ la maison est rose. c) M. Laurent travaille _____________ la journe. d) Elle mange ________________ les jours. e) ________ le monde aime ce film. f) Mon pre parle ____________ le temps. g)Il comprend _________la leon. h)J'achte ________les glaces pour mes amis. What does the reader learn from Athenes perspective? Check all that apply. calculate the molarity of a solution containing 15.2 grams of nacl dissolved in 2.5 l of solution How did Executive Order 8802 affect civil rights reform? A) It designated war zones from which anyone could be removed. B) It allowed Japanese Americans to enlist in the armed forces. C) It stated that jobs in the aircraft industry would remain segregated. D) It assured fair hiring practices in any job funded with government money. Dogstuff adjusts salaries based on changes in its stock price, which has increased consistently at one fifth its value per year. Yearly raises are the same fraction of the current salary as the yearly fractional change in stock prices. Hector currently earns $31 comma 500 per year at Dogstuff. Find last year's salary, the salary in 2 years, and the salary 2 years ago. Using a Graph to Find Positive or Negative Intervals Is Lmn=OPQ? If so, name the congruence postulate that applies. Read the excerpt to answer the question. "We want more school houses and less jails; more books and less arsenals; more learning and less vice; more constant work and less crime; more leisure and less greed; more justice and less revenge; in fact, more of the opportunities to cultivate our better natures, to make manhood more noble, womanhood more beautiful and childhood more happy and bright. These in brief are the primary demands made by the Trade Unions in the name of labor. These are the demands made by labor upon modern society and in their consideration is involved the fate of civilization."Background information: Samuel Gompers was an important labor leader in the 1800s. Which statement best reflects the main idea of the excerpt?A) Modern society is too concerned with the fate of civilization.B) Unions are working toward helping workers attain a better life. C)The only way workers can achieve higher wages is through the labor movement. D) Economic growth is the key to improving peoples standard of living.