Here , we are provided with a table which shows 5 consecutive terms of an arithmetic sequence . But before solving further , let's recall that ;
The n'th term of a Arithmetic Sequence let's say it be
is given by ;
Where , <u>d</u> is the common difference
Now , here we are given with ;
We have to find the 2nd , 3rd and 4th term respectively ,
Now , by using the above formula , 5th term can be written as ;
Putting the values and transposing 1st term to RHS , we have ;
Now , as we got the common difference , so we can find out the missing terms now ;



Now



Also ,



Now , The given table can be written as ;

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Answer:
[Vertex form]
Step-by-step explanation:
Given function:

We need to find the vertex form which is.,

where
represents the co-ordinates of vertex.
We apply completing square method to do so.
We have

First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.


Isolating
and
terms on one side.
Subtracting both sides by 15.


In order to make the right side a perfect square trinomial, we will take half of the co-efficient of
term, square it and add it both sides side.
square of half of the co-efficient of
term = 
Adding 36 to both sides.


Since
is a perfect square of
, so, we can write as:

Subtracting 21 to both sides:


Dividing both sides by -3.

[Vertex form]
Answer:
n = -7,6
Step-by-step explanation:
n(n+1)+3=45
distributive property: a(b+c) = ab+ac
n²+n+3 = 45
n²+n -42 = 0
factor now
(n+7)(n-6) = 0
n = -7,6
Answer:
para el primer dibujo seria 1/12
para el segundo dibujo seria 1/16
para el tercer dibujo seria 1/10, pero tengo dudas con esta porque no se ve toda la figura.
Step-by-step explanation:
Answer:
1) y = 5/2x - 3/2
2) y = 2/5x - 4/5
Step-by-step explanation:
1)
(1, 1) and (3, 6)
m = (y2 - y1)/(x2 - x1)
m= (6 - 1)/(3-1)
m= 5/2
m= 5/2
y - y1 = m(x - x1)
y - 1 = 5/2(x - 1)
y - 1 = 5/2x - 5/2
y = 5/2x - 3/2
2)
(2, 0) and (7, 2)
m = (y2 - y1)/(x2 - x1)
m= (2 - 0)/(7 - 2)
m = 2/5
y - y1 = m(x - x1)
y - 0 = 2/5(x - 2)
y = 2/5x - 4/5