Simplify the expression: 1.8-8.8g+7g+10.4+5.3g
1 answer:
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2018 is the 70th term of the progression.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
Answer:
Part a) The solution is the ordered pair (6,10)
Part b) The solutions are the ordered pairs (7,3) and (15,1.4)
Step-by-step explanation:
Part a) we have
----> equation A
----> equation B
Multiply equation A by 10 both sides to remove the fractions
----> equation C
isolate the variable y in equation B
----> equation D
we have the system of equations
----> equation C
----> equation D
Solve the system by substitution
substitute equation D in equation C
solve for x
Multiply by 3 both sides
Combine like terms
<em>Find the value of y</em>
The solution is the ordered pair (6,10)
Part b) we have
---> equation A
----> equation B
isolate the variable x in the equation B
----> equation C
substitute equation C in equation A
solve for y
Solve the quadratic equation by graphing
The solutions are y=1.4, y=3
see the attached figure
<em>Find the values of x</em>
For y=1.4
For y=3
therefore
The solutions are the ordered pairs (7,3) and (15,1.4)
