the 11th term of an arithmetic sequence is 57 and the sum of the first and fourth term is 29. determine the first three terms of the sequence, the formular of nth term​

Let a (n) denote the n-th term of the sequence. Since the terms form an arithmetic sequence, you have

a (n) = a (n - 1) + d

for some fixed constant d. You can write any term in the sequence as a function of the first term:

a (n) = [a (n - 2) + d] + d = a (n - 2) + 2d

a (n) = [a (n - 3) + d] + 2d = a (n - 3) + 3d

and so on, down to

a (n) = a (1) + (n - 1) d

so given that a (11) = 57 (so that n = 11), you have

a (1) + 10d = 57 … … … [1]

The sum of the first and fourth terms is 29:

a (1) + a (4) = 29

but we can write a (4) in terms of a (1) :

a (1) + [a (1) + 3d] = 29

which gives us another equation in a (1) and d :

2 a (1) + 3d = 29 … … … [2]

Now solve [1] and [2] :

-2 (a (1) + 10d) + (2 a (1) + 3d) = -2 (57) + 29

-17d = -85

d = 5

a (1) + 10d = a (1) + 50 = 57

a (1) = 7

Then the n-th term of the sequence is given by

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

i don’t know how to solve this and i need help

Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the
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3,12,3, 11,5,5, 3, 10, 12

pattern x starts with the number 0 and follows the rule "add 2". pattern y starts with the number 30 and follows the rule "subtract 5". place a check mark in the box next to each ordered pair that that could be formed by the corresponding terms in the patterns
A. [2, 5]
B. [4, 20]
C. [10, 5]
D. [12, 0]
E. [15, 22]
F. [6, 15]

Greg has a storage container in the shape of a
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What is the measure of AB?

If = cos + (3 − 2

2

) − (3 + 2), find

2

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i need help! i provided the problem in the picture

Which statement defines Suppose that farmers grew an unexpectedly large number of tomatoes this year. How would this increase in production affect the price of tomatoes?the term markup?

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eight (8)÷ by nine (9) ​

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Please need help ASAP.

Subtract. 82.6 - 27.9​

a restaurant offers 4 pasta meals, 5 seafood meals, and 6 burgers for its main course. If a diner picks a meal at random, what is the probability that the meal selected is seafood

Can someone please help me I will mark u brilliant

Reem is 5 years older (bigger) than 3 times Sara's age.
If Reem is 28 years old, how old is Sara?

Can someone please help

someone please help.
find the angle between the given vectors to the nearest tenth of a degree

u=<-5,-4>, v=<-4,-3>

a: -9.1
b: 1.8
c: 0.9
d: 11.8

250 employees in an organization were surveyed about their hair color and height. The data collected is presented in the table. If a person is selected at random, what is the probability that the person is taller than 180 centimeters and has black hair?

A) 0.257

B) 0.351

C) 0.360

D) 0.116​

someone pls help with this equation (subtract the following two equations, to eliminate the x variable then solve for y) ILL MARK YOU BRAINLIEST!!!

NO LINKS OR ELSE YOU'LL BE REPORTED! Please give me the correct answer.Only answer if you're very good at math.
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Well this is very hard and I need help passing do anybody know the answer to this question

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A survey was run by a high school student in order to determine what proportion of mortgage-holders in his town expect to own their house within 10 years. He surveyed 35 mortgage holders and found that the proportion of these that did expect to own their house within 10 years is 0.51. The student decides to construct a 95% confidence interval for the population proportion. a)Calculate the margin of error that the high school student will have. Give your answer as a decimal to 2 decimal places. Margin of error

Une coopérative vend un important lot d’œufs de trois tailles différentes.
20 % des œufs sont petits, 50 % sont moyens et 30 % son gros.
Les œufs sont de deux qualités : - « extrafrais » car pondus depuis moins de 9 jours ;
- « frais » car pondus entre 10 et 28 jours plus tôt.
On a remarqué que : ▪ 80 % des petits œufs sont extrafrais ;
▪ 50 % des œufs moyens sont extrafrais ;
▪ 20 % des gros œufs sont extrafrais.
Dans ce lot, on prélève un œuf au hasard et on note sa taille puis sa qualité.
On nomme respectivement P, M et G les événements « l’œuf choisi est petit », « l’œuf choisi est
moyen » ; « l’œuf choisi est gros » et on appelle E l’évènement « l’œuf choisi est extrafrais ».
1) Construire l’arbre de probabilité traduisant la situation.
2) Quelle est la probabilité d’obtenir : a. un petit œuf extrafrais ? b. un petit œuf frais ?
3) Quelle est la probabilité de choisir un œuf extrafrais ?
Aide moi svp

By midweek, Wendy had spent $46.65. At the end of the week, she had spent $23.35 more. How much did Wendy spend that week?

PLS TELL ME WHAT IT IS

What is the greatest common factor of the polynomial -25y^3+15y^2-5y

Consider the following expression.
3y + 5x + 2
Select all of the true statements below :
2 is a constant.
3y and 2 are like terms.
3y + 5x + 2 is written as a sum
of three terms.
3y is a coefficient.
3y is a factor.
None of these are true.

Select the correct answer.
What is the equation of the asymptote for this function?
Ax) = In x + 5
O A.
x=0
B.
x= -5
O c.
y= 0
OD.
y=-5