Evaluate the expression when x = 3 and y=-7. x-8y
1 answer:
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The first term in a sequence is sometimes referred to as as opposed to
because
represents the initial value
The question refers to the difference between the terms
and
The terms in a sequence are represented by a subscript number.
Take for instance a₂ or T₂ represents the second term.
However, when the first term is represented by a₀ instead of a₁.
It means that the sequence has an initial value, other than the first term.
Even though the words "first" and "initial" are synonyms, they do not entirely represent the same thing.
Take for instance, a₀ can be used instead of a₁ in the following scenario
<em>The population of a country is 1000 in 1996 and The country experiences an increment of 250 people every year after 1996.</em>
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The above means that:
a₀ = 1000 --- the initial year
a₁ = 1000 + 250 = 1250 ---- the first year after 1996 (i.e. 1997)
Read more about sequence at:
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So for this problem we can recognize that it's a system of linear equations
recall the slope intercept form of a line
given the info we can write two linear equations one for John and one for Lyndon
take a look at johns part of the question. we can see that his bank starts with 100 dollars and every day after he saves 20 dollars. Now we can see that the 100 is the y intercept or b of our equation because it's our initial amount and the rate of change or m of the equation is 25. filling in this info we get this as johns equation:
now we can do the same for Lydon, she has 50 dollars to start and saves 30 dollars a day. So using the same steps as we did for John we get the equation
now we can do a little trick, to find out when their bank amounts will be equal we set both equations equal to each other (we're just substituting y into the equation) So we get
now let's clean this up and solve for X with some algebra
subtract 25x
combine like terms
subtract 20
divide off 5 to get your x value
now we're almost done we just need to plug X back into any of our two equations we made at the beginning of the problem lets use johns equation and plug in 16 because as we found out x=16
multiply and add to get
now that we know
we can finalize our answer answer to the system as a coordinate (x,y) and we'll get
(16,500)
since the questions asks after how many weeks though we would say 16 or the x value because in a time related problem, time is always the x value so the final answer is
recall the slope intercept form of a line
given the info we can write two linear equations one for John and one for Lyndon
take a look at johns part of the question. we can see that his bank starts with 100 dollars and every day after he saves 20 dollars. Now we can see that the 100 is the y intercept or b of our equation because it's our initial amount and the rate of change or m of the equation is 25. filling in this info we get this as johns equation:
now we can do the same for Lydon, she has 50 dollars to start and saves 30 dollars a day. So using the same steps as we did for John we get the equation
now we can do a little trick, to find out when their bank amounts will be equal we set both equations equal to each other (we're just substituting y into the equation) So we get
now let's clean this up and solve for X with some algebra
subtract 25x
combine like terms
subtract 20
divide off 5 to get your x value
now we're almost done we just need to plug X back into any of our two equations we made at the beginning of the problem lets use johns equation and plug in 16 because as we found out x=16
multiply and add to get
now that we know
we can finalize our answer answer to the system as a coordinate (x,y) and we'll get
(16,500)
since the questions asks after how many weeks though we would say 16 or the x value because in a time related problem, time is always the x value so the final answer is