In an arithmetic sequence, the sum of the 3rd and 8th term is 1. Given that the sum of the first seven terms is 35, determine the first term and the common difference.

Answers

Answer 1

Answer:

           first term:    a₁ = 14        the common difference:  d = -3

Step-by-step explanation:

The sum of the 3rd and 8th term is:

                                                            [tex]a_3+a_8=1\\\\a_1+2d+a_1+7d=1\\\\\underline{2a_1+9d=1}[/tex]

The sum of the first seven terms is 35:

                                                           [tex]S_7=35\\\\\dfrac{a_1+a_7}2\cdot7=35\\{}\qquad\quad^{\div7\qquad\div7}\\ \dfrac{a_1+a_1+d}2=5\\{}\qquad\qquad^{\cdot2\qquad\cdot2}\\2a_1+6d=10\\{}\qquad\ ^{\div2\qquad\div2}\\a_1+3d=5\\{}\quad\ ^{-3d\quad\ -3d}\\a_1=5-3d[/tex]

[tex]2a_1+9d=1\\\\2(5-3d)+9d=1\\\\10-6d+9d=1\\{}\qquad\qquad^{-10\quad-10}\\{}\qquad3d=-9\\{}\qquad^{\div3\qquad\div3}\\{}\qquad d=-3\\\\\\a_1=5-3(-3)=5+9=14[/tex]


Related Questions

how many abtuse angles are there in a right angle?

Answers

Answer:

None

Step-by-step explanation:

In a right triangle there is one 90-degree angle and the other two have to be acute because the angles have to sum to be 180 degrees.

What is: 8x + 7 - 3x

Answers

Answer: 5x + 7

Step-by-step explanation:

Combine like terms

PLEASE HELP ME ASAP !!!!!!!!!!!!!!!!!

Answers

Answer:

rational numbers

Step-by-step explanation:

all numbers are rational, but not all numbers are integers or whole numbers.

-1/2y=1/2+5 what is the solution?

Answers

Answer:

-11

Step-by-step explanation:

-1/2y=1/2+5

- 1/2 y = 1+10 (by taking lcm)

               2  

 [tex]\frac{-1}{2}[/tex] x 2y = 11

y = -11

[tex] \frac{ - 1}{ \: \: \: 2} y = \frac{1}{2} + 5[/tex]

[tex] \frac{ - 1}{ \: \: \:2} \times y = \frac{1}{2} + 5[/tex]

[tex] \frac{ - 1}{ \: \: \:2} \times y = \frac{11}{2} [/tex]

[tex]y = \frac{11}{2} \div \frac{ - 1}{ \: \: \:2} [/tex]

[tex]y = \frac{11}{2} \times \frac{ \: \: \: 2}{ - 1} [/tex]

[tex]y = \frac{ \: \: 22}{ - 2} [/tex]

[tex]y = - 11[/tex]

The value of y = -11

Therefore :-

[tex] \frac{ - 1}{ \: \: \:2} \times - 11 = \frac{1}{2} + 5[/tex]

2. Camilla adds 2 cucumbers for every 5 tomatoes in a veggie mix. What
is the ratio comparing cucumbers to tomatoes? *

Answers

2:5

A ratio is an amount to an amount. It said 2 to every 5 cucumbers. 2:5 is your answer

It’s two parts help meeee please

Answers

Answer:

m∠RMS = 20°

Step-by-step explanation:

Find ∠RMS and look at the two values it crosses.

∠RMS crosses through 180 and 160.

Find the difference between the two values to get the measure:

180 - 160 = 20°

So, m∠RMS = 20°

(Its also an acute angle.)

Answer:

20

Step-by-step explanation:

The mistake is in using 160 as the answer. It isn't.

The angle is very small well under 90. It is acute.

The horizontal part of the angle is on 180 degrees of the protractor.

Therefore the angle size is 180 - 160 = 20 degrees.

Gianna, Jada, and Brittney and a bunch of other friends had a horseshoe competition. Jada and Brittney were eliminated after two rounds because they were too busy texting but Gianna went onto round eight to win 47 pieces of gum. Later, she gave two to each of her friends. She only has 1 remaining. How many friends does she have?

Answers

Answer:

23 friends

Step-by-step explanation:

Let the number of friends she has = x

Total number of gum = 47 pieces

She gave 2 each to her friends, hence:

2x + 1 = 47

2x = 47 - 1

2x = 46

x = 46/2

x = 23

Therefore, the number of friends she has is 23

Pedmas
When solving Pedmas and there are brackets inside brackets what should you do to get the operations right?

13POINTS!!
Could mark as brainelist

Answers

Answer:

Step-by-step explanation:

You do what's in the innermost brackets first, unless you have an unknown variable.

If x + y = 13 and y = 2, then which of the following is true according to the
substitution property?
OA) 2 + y = 13
B) x= 13- y
OC) x+ 2 = 13
OD) y = 13 - x

Answers

Answer:

b

Step-by-step explanation:

Will give brainliest!

Answers

I think it’s B.1/2:)

Simplify:
3(8) ° . (3) -2

Answers

3 x 8 = 24

3 x -2 = -6

reply if you this was wrong or you needed a different answer pls >:(

Which of the following are equivalent to
- 5/10?
A)- 1/2.
B)-5/-10.
C)- (4/8).
D)-0.5.
E)5/-10.

Select all that apply.​

Answers

A B and E i think I’m sorry if you get this wrong :( have a good day!

  a,b and e  Read the paragraph from The Evolution of Useful Things.

In 1916 the company's sales manager insisted that a laboratory be formed to carry out experiments and tests to ensure quality control so that salesmen would not be embarrassed by faulty products. The laboratory in time made possible the research and development necessary to produce new and improved items in response to problems experienced by sandpaper users.

Which words from the excerpt indicate an order of the events in this paragraph?

In 1916, to carry out

to carry out, ensure

so that, in time

In 1916, in time

Find the slope of the line given two points:
(8, 10) and (-7, 14)
A
m = -15/4
B
m = -24/1
с
m = -4/15
D
m = 4/15

Answers

Answer:

The answer is option C

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(8, 10) and (-7, 14)

The slope is

[tex]m = \frac{14 - 10}{ - 7 - 8} = \frac{4}{ - 15} = - \frac{4}{15} \\ [/tex]

We have the final answer as

[tex] - \frac{4}{15} \\ [/tex]

Hope this helps you

30 POINTS + BRAINLIEST TO FIRST CORRECT ANSWER!
The ratio table below shows the relationship between the number of bricks in a wall and the length of the wall.
Brick Wall
Number of bricks Length (ft)
6 3
8 4
12 6
18 9
When the number of bricks is multiplied by 2, the length is multiplied by
1.
2.
3.
6.

Answers

Answer:

The length will be multiplied by 2.

Step-by-step explanation:

By looking at the first and third ratio, we know that the no. of birck have been multiplied by 2 and the length has also been multiplied by 2 .

So when the number of bricks is multiplied by 2, the length is multiplied by 2

Answer:

2

Step-by-step explanation:

Using the table we observe the points

(6, 3) and (12, 6)

The number of bricks doubled

6*2 = 12, and

The length is doubled accordingly

3*2 = 6

So the answer is 2

what is 1372678590643754873564132`4526786957586534315267489557654356478392837465647389485767483994587675483993847654378299485764738293847643728237464732823456789087654321234567890-098765432234567890876543212345678909876543223456789087654321234567899876543212345678909876147687628750-2598765246468759809-50897`86574894`702`427`0849`624`0-02`7968139750805831356139856585965.1*564738291092837465748392983745657483922376447382837465473823476547832938475647838476547882376547382983746546372819127635672819928375463728192736453627189237454637281927364563728127364564738292837456473829=



ANSWER AND YOUR TE BRAINLIEST by the way round this to the nearest quadrillion.

Answers

Answer:

HAHAHAHAHA!!!!!!!! Yeah right! LOL

Step-by-step explanation:

Answer:

69420 :)

Step-by-step explanation:

1372678590643754873564132`4526786957586534315267489557654356478392837465647389485767483994587675483993847654378299485764738293847643728237464732823456789087654321234567890-098765432234567890876543212345678909876543223456789087654321234567899876543212345678909876147687628750-2598765246468759809-50897`86574894`702`427`0849`624`0-02`7968139750805831356139856585965.1*564738291092837465748392983745657483922376447382837465473823476547832938475647838476547882376547382983746546372819127635672819928375463728192736453627189237454637281927364563728127364564738292837456473829 is 69420 rounded to nearest quadrillion is juan

A shirt cost $18.99 with a 6.5% sales tax. What is the final cost?

Answers

Answer:

$20.22

Step-by-step explanation:

You multiply 18.99 with 0.065 to see how much extra money you have to pay. Then you add it back to 18.99 for the final cost.    

The price per share of a professional sports team increased from $58 to $65 over the past year. What is the stock’s percent increase during this time? Round your answer to the nearest percent.

Answers

Answer:

12%

Step-by-step explanation:

amount of change/original value×100%

note: any thanks would be appreciated. thank you!

solve 8 + 7x = 14
solve y + (-12) = 10

Answers

Answer:First one is x=1

second is y=22

Step-by-step explanation:

Answer:

[tex]x = \frac{6}{7}[/tex]  y = 22

Step-by-step explanation:

For first equation:

Subtract 8 from each side, so it now looks like this: 7x = 6Divide each side by 7 to cancel out the 7 next to x. It should now look like this: [tex]x = \frac{6}{7}[/tex]  

For second equation:

Simplify: y - 12 = 10Add 12 to each side, so it now looks like this: y = 22

I hope this helps!

5) Ana medía 1,42 m a principios de año. Pasados tres meses, medía 1.45 y a finales de
año, 1,51. ¿Cuándo creció más rápido, en los primeros tres meses o en el resto del
año?

Answers

solución:
creció más rapido en los primeros tres meses

explicación:
creció 1 cm (.01m) por mes en los primeros tres meses y creció 2/3 cm
(.0067m) por mes en el resto de año

630 divided 18 please I need to know ASAP!!

Answers

Answer:

35 :)

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

D = Divide

M = Multiply

S = Subtract

B = Bring down

Line L is Parallel to Line M. Find the value of x and y (pls help asap)

Answers

10x-17 = 8x+1 (vertical angles)
2x = 18
x = 9

plug in to find angle measure
8(9)+1 = 73

73 + 6y + 29 = 180 (supplementary angles)
102 + 6y = 180
6y = 78
y = 13

The value of the variables 'x' and 'y' will be 9 and 13, respectively.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Line L is Parallel to Line M.

The vertical opposite angles (10x - 17) and (8x + 1) are equal. Then the equation is given as,

10x - 17 = 8x + 1

Simplify the equation, then the value of 'x' will be given as,

10x - 8x = 17 + 1

2x = 18

x = 9

The angle (6y + 29) and (8x + 1) are the supplementary angles. Then equation is given as,

6y + 29 + 8x + 1 = 180

6y + 29 + 8(9) + 1 = 180

6y + 102 = 180

6y = 76

y = 13

The value of the variables 'x' and 'y' will be 9 and 13, respectively.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Solve for m.

5 + 2m = 9

Answers

Answer:

m = 2

Explanation:

how is the translation of a figure on a grid different from a reflection of a figure?​

Answers

Answer:

This means that on the coordinate plane, the coordinates for the vertices of the figure will change. To graph a translation, perform the same change for each point. ... In a reflection, the figure flips across a line to make a mirror image of itself.

Step-by-step explanation:

simplify.show work
9(20-3·8)-4²


thank you gggggggggggg

Answers

Answer:

9(20−(3)(8))−42

=9(20−24)−42

=(9)(−4)−42

=−36−42

=−36−16

=−52

The answer is -20 not what that other guy said.

worth 20 points! need help badly

Answers

Answer:

Step-by-step explanation:

FIRST ONE GOES WITH 5TH ONE 2 ONE GOES WITH 1 ONE AND LAST ONE GOES WITH 4 TH ONE

select all input values for which f(x)=3

Answers

Answer:

Step-by-step explanation:

x=-3

Answer:

x=3

Step-by-step explanation:

3.2666 rounded to the nearest hundredth

Answers

Answer:

3.27

Step-by-step explanation:

Hope it helps!!!

Simplify using the distributive property:
6(y-8)
IM GIVING BRAINLIEST

Answers

Answer:

6y - 48

Step-by-step explanation:

6 times y its 6y

6 times -8 is -48

You cannot solve further without knowing the variable

Answer; 6y−48

Step-by-step explanation:

Please answer 5-8 ASAP I will give brainliest

Answers

Answer:

5. m∠A = 26

6. m∠D = 118

7. m∠E = 43

8. m∠H = 85

Step-by-step explanation: complementary= 90 supplementary = 180

5. (2x - 8) + (4x +4) = 90

6x - 12 = 90

6x = 102

x = 17

m∠A = 2x - 8  

m∠A = 2(17) - 8 = 26

6. (2x + 18) + (5x + 8) = 180

7x + 26 = 180

7x = 154

x = 22

m∠D = 5x + 8

m∠D = 5(22) + 8 = 118

7. (2x + 15) + (3x + 5) = 90

5x + 20 = 90

5x = 70

x = 14

m∠E = 2x + 15

m∠E = 2(14) + 15 = 43

8. (5x - 20) + (4x + 7 ) = 180

9x - 27 = 180

9x = 207

x = 23

m∠H = 4x -7

m∠H = 4(23) - 7 = 85

The average price of a movie ticket in the United States from 1980 to 2000 can be modeled by the expression, 2.75+0.10x, where x is the number of years since 1980. Which part of the expression corresponds to the cost of movie tickets in 1980?

Answers

Answer:

$4.7

Step-by-step explanation:

step one:

Let the cost be y

to solve for the cost of  a movie ticket, we need to solve the expression

y=2.75+0.10x

step two:

given that x is the number of years between 1980-2000

the number of years is 20years

put x= 20 in the expression for the cost we have

y=2.75+0.10(20)

y=2.7+2

y=$4.7

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