Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
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The 20th term is f(20):
f(20) = 20^2 +1 = 401
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<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
Answer:
(-∞,0)
Step-by-step explanation:
Graph y=|x|
Note that the graph is shaped like a V. The left half of the graph is decreasing from -∞ up until 0 when it hits the origin and starts to increase. Put this into interval notation: (-∞,0).
The answer is C because it’s constant but starts further down
Answer: Expression represents the number of text messages you sent on Tuesday = 2x
Expression represents the number of text messages you sent on Wednesday = 12+2x
Expression represents the number of text messages you sent on Thursday = x+6
Step-by-step explanation:
Given:
Number of text messages sent on Monday = x
On Tuesday, Number of text messages sent = 2 (Number of messages sent on Monday)
= 2 x
On Wednesday, Number of text messages sent = 12+ (Number of messages sent on Tuesday)
= 12 +2x
On Thursday, Number of text messages sent = 
= x+6
Expression represents the number of text messages you sent on Tuesday = 2x
Expression represents the number of text messages you sent on Wednesday = 12+2x
Expression represents the number of text messages you sent on Thursday = x+6
All you gotta do is add up the two sides and then subtract it from 47.3 .
So 10+17.3= 27.3
47.3-27.3= 20
