What is the explicit formula represented by this graph?

a) an = −1 − 1 (n−1)
b) an = 1 + 1 (n−1)
c) an = 3 + 2 (n−1)
d) an = 3 − 2 (n−1)

aₙ = 3 + 2(n - 1)

Step-by-step explanation:

The points fall on a straight line, so we have an arithmetic sequence.

The explicit formula for an arithmetic sequence is

aₙ = a₁ + d(n -1 )

Data:

a₁ = 3

a₂ = 5

Calculations:

d is the difference in value between two consecutive terms.

For example,

d = a₂ - a₁ = 5 - 3 = 2

Insert the value of d

aₙ = a₁ + 2(n -1 )

Insert the value of a₁

aₙ = 3 + 2(n - 1)

Note: This sequence starts with n = 0, but the formula still works.

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1