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

(15 POINTS+ BRAINLIEST)
How do you know if a set of information shows a proportional relationship? Select ALL that apply.

Answers

Answer:

(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

Step-by-step explanation:

google

and I know that the second one is the answer I dont know the others

Round to 4,725.806
Answer the question

Answers

Answer:

Step-by-step explanation:

Your question is incomplete.  Are you rounding to the nearest 100?  nearest 100,000?

4725806 to the nearest thousand is 4725800.

4725806 to the nearest unit is 4725806.

                 to the nerest ten is 4725810.

If f=(9/5 x c ) +32 85c =__f

Answers

Answer:

185

Step-by-step explanation:

Answer:

It entirely depends upon an individual.

It’s a known fact that humans need social interaction. Lack of which can affect their social behaviour and mindset. Whilst most would agree that e-learning is widely preferred by the younger generation, it is undeniably detaching them from social interactions.

When kids or students are engrossed in learning online, they’re missing out on social interactions that can open various doors of the mind, be it creative or observational skills. It’s understood that e-learning allows an individual to study far and beyond the subject and gives them an opportunity to explore multiple fields of their interest, one can’t ignore that it chains them to the system as well.

The deal-breaker in such a situation is an individual. If they demand social interaction, they would keep their digital device aside for once and would get indulge in social interaction. If they’re of another kind, they would prefer spending their days and nights just exploring and reading about new things online.

So, in my opinion, it’s quite subjective to narrow down the overall benefits and drawbacks of e-learning.

I hope I have answered your question.

John has a soup recipe that calls for two 14.5-ounce cans of chicken broth. The recipe serves 4 people. He wants to increase the recipe to serve it to a party of 28 people. If John buys chicken broth in 1-quart containers, how many containers does he need?

Answers

Answer:

  6 11/32

Step-by-step explanation:

The two cans of broth used in the recipe total 2·14.5 oz = 29 oz. The number of people John wants to serve is 28/4 = 7 times the number served by one recipe. So, the amount of broth needed is ...

  (29 oz)·7 = 203 oz

Each quart container of broth holds 32 oz, so John will need ...

  (203 oz)/(32 oz/container) = 6 11/32 containers

John needs 6 11/32 containers of broth.

_____

If John must buy the broth, he must buy 7 containers. he will have 21/32 of a container left over after making his soup.

6 = x + 2/3
Show your work please;w;

Answers

Answer:

x = 5 1/3

Step-by-step explanation:

6 = x + 2/3

-2/3 -2/3

5 1/3 = x

Answer:

[tex]\boxed {x = \frac{16}{3}}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]6 = x + \frac{2}{3}[/tex]

-Switch sides:

[tex]6 = x + \frac{2}{3}[/tex]

[tex]x + \frac{2}{3} = 6[/tex]

-Subtract [tex]\frac{2}{3}[/tex] to both sides and convert 6 to a fraction:

[tex]x + \frac{2}{3} - \frac{2}{3}= 6 - \frac{2}{3}[/tex]

[tex]x = \frac{18}{3} - \frac{2}{3}[/tex]

-Since both fractions have the same denominator, then you subtract the numerators:

[tex]x = \frac{18 - 2}{3}[/tex]

[tex]\boxed {x = \frac{16}{3}}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]\frac{16}{3}[/tex].

I really Need Help..

Answers

Answer:

Y= -1.2x

Step-by-step explanation:


What is the slope of the line that passes through the points (3,-2) and (1,8)

Answers

Answer:

10/-2= -5

Step-by-step explanation:

slope= change of y/ change of x

John has 1,000 v-bucks and he earns 20 weekly. Aaron has 600 v-bucks and 50 weekly. After how many weeks will Aaron have more v-bucks then John? Choose the Inequality that matches this scenario

Answers

Answer:

D

Step-by-step explanation:

2x+7=x+3 solve for x

Answers

Answer:

x = -4

Step-by-step explanation:

Rearrange equation so that like terms are on one side and the numbers are on the other.

2x - x = 3 - 7

x = -4

Answer:

x=-10

Step-by-step explanation:

2x-x+7=x-x-3

x+7-7=-3=7

x=-10

Heelppp plzzzz I need help

Answers

Answer:

5 i think can i see the choices

Step-by-step explanation:

I think 5 but I don’t really know. Sorry

What is 3 3/5 divided by 2 1/4? :)

Answers

Answer:

1.6 or 8/5

Step-by-step explanation:

What is the equation of the line?
Explain.​

Answers

Answer:

y = -2/1x-2

Step-by-step explanation:

If each unit happens to be 1 then this will be correct, but it is hard to determine the equation without units.

I don’t understand could anyone help me solve? And maybe an explanation?

Answers

Your answer would be B

(Please give me brainliest

f(x)=x+6 when x= -2, 0, and 5.

f(-2)=__

f(0)=__

f(5)=__

^ I have no idea how to solve this and if your supposed to sub the values into both x's or just one. please help!​

Answers

Answer:

5

Step-by-step explanation:

10 – 7x = 2 - 8x help :)

Answers

10-7x=2-8x

We move all terms to the left:

10-7x-(2-8x)=0

We add all the numbers together, and all the variables

-7x-(-8x+2)+10=0

We get rid of parentheses

-7x+8x-2+10=0

We add all the numbers together, and all the variables

x+8=0

We move all terms containing x to the left, all other terms to the right

x=-8

Which shows the number subsets to which the number
- v144 belongs?

Answers

Answer: 3

Step-by-step explanation:

I'm smart

Madison is starting her own sewing business. Madison thinks she will do a better job than her competitors, so she thinks she can charge $13.05 per hour. If she knows she will only be able to work 190 hours per month (that's 47.5 hours per week), how much money will she earn each month?

Answers

Answer:

$2479.5

Step-by-step explanation:

In this problem we will estimate her monthly earnings

given that she earns $13.05 per hour

and also given that she works for 190 hours in a month

then in a month, her earnings will be

=$13.05*190

=$2479.5

alternatively,

per week she works 47.5hours

in a week she will earn 13.05*47.7= $622.485

4 weeks make a month

then after one month her earning will be

$622.485*4= $2479.5

At a bakery, Victor makes 20 cupcakes. He puts them
in equal rows with 10 cupcakes in each row. Which
calculation can be used to find the number of rows of
cupcakes Victor makes?

Answers

Answer:

20/10 equals 2 rows. This is division

Step-by-step explanation:

Since you have 20 cupcakes and you put 10 in each row, you have to divide 20/10=2. This is your calculation.

I NEED HELP PLEASE WITH NUMBER 7

Answers

Answer:

this question cannot be solved

Answer:

183

Step-by-step explanation:

Sub the values into the expression

-(-3)² - (-3)(8²)

-9 - (-192)

-9 + 192

183

a rectangle is 3x feet long and 4feet wide.the value of the perimeter (in feet) is equal to the value of the area in square feet. find x

Answers

Answer:

x = [tex]\frac{4}{3}[/tex]  

Step-by-step explanation:

Rectangle:

Length = 3x feet

Width = 4 feet

Perimeter = 2*(length +width)

                = 2* (3x + 4)

                = 2*3x + 2*4

                 = 6x + 8

Area = length * width

        = 3x * 4

        = 12x

Area of rectangle =  perimeter of rectangle

                       12x = 6x + 8              {Subtract 6x form both sides}

               12x - 6x  = 8

                       6x = 8                    {Divide both sides by 6}

                         x = 8/6

                         x = [tex]\frac{4}{3}[/tex] feet

Answer:

3 feet x 4 feet= 12 feet

Step-by-step explanation:

Plz help! I will mark you brainliest!

Answers

Answer:

  A.  80

Step-by-step explanation:

No math necessary. You know the brace needs to be longer than the distance between posts, so cannot be 4, 15, or 42 inches. The only answer choice longer than 64 inches is the correct one:

  80 inches

I NEED HELP!!!! ASAP

Answers

Answer:

21

Step-by-step explanation:

1. (-4)2= 16

2.15/(-3)= 5

3. 16+5=21

Answer:

11

Step-by-step explanation:

First do -4^2

Then divide -15 and -3

Then 16-5

11

What is the slope of all lines parallel to the line 16x20y = 9?

Answers

Graph the line using the slope and y-intercept, or two points.
Slope:
−4/5

PLS HELP ME! Convert the following graph into a table.

Answers

Step-by-step explanation:

(3,3)(2,1)(1,3)(0,3)

Or the other way around

(0,3)

(1,3)

(2,1)

(3,3)

by the way this is a function because all the outputs have one input. Nothing is being shared.

5x+5y are like terms and can be added together to simplify to 10xy


A.True
B.False

Answers

Step-by-step explanation:

B. False

they cannot be written as 10xy but only in 5x+5y

x and y will only become together if they are multiplied

as you can see there's a plus sign

you can add them if it is in 5x+5x (or) 5y+5y but never as in 5x+5y

Find the sum or difference of the polynomials (x2−xy+y2) − (x2+xy+y2)

Answers

The correct answer is-2xy if it’s subtract

Quentin is planning a party. The event coordinator charges a base fee of $67 and an additional $18.50 per party guest. If Quentin has less than $400 to spend on the party, which of the following best describes all the possible numbers of guests (g) that he can invite?

Answers

Answer:

g=20

Step-by-step explanation:

Answer:g=<25

Step-by-step explanation:

f(x)=x^2+8x+15/2x^2+11x+5
state the equations for the vertical and horizontal asymptotes of the graph y=f(x)

Answers

Answer:

Step-by-step explanation:

.. What type of number is the following?
24i+16
A. Real
B.purely
C.complex
D. Not enough information

Answers

Answer:

Step-by-step explanation:

The i is usually the square root of -1 which does not exist in the real number system.

The number given is a mixture of real and complex and is classified as complex.

The answer is C

Answer:

the answer is: C,Complex

Step-by-step explanation:

Complex Numbers

A Complex Numbers is a combination of a real number and an imaginary number in the form a + bi. The real part is a, and b is called the imaginary part.

Examples include 4 + 6i, 2 + (-5)i, (often written as 2 - 5i), 3.2 + 0i, and 0 + 2i.

Note the last two examples:

3.2 + 0i is just the real number 3.2. All real numbers are complex numbers with zero for the imaginary part.

0 + 2i is just the imaginary number 2i. All imaginary numbers are complex numbers with zero for the real part.

I hope it helps you lot!!!

What is the measure of angle 2?

Answers

142 degrees

Vertical angles are congruent

Answer:

142

Step-by-step explanation:

they are the same length

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