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What is the equation of the line that passes through (-3, 6) and has a slope of -2?
First, we need to write the equation of the line in point-slope form:-
Replace y1 with 6, m with -2, and x1 with -3:-
On simplification,
On further simplification,
Add 6 on both sides:-
<h3>Good luck with your studies.</h3>
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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.
Given:
Side length = 12 in
To find:
The area of the regular polygon.
Solution:
Number of sides (n) = 6
Let us find the apothem using formula:
where s is side length and n is number of sides.
Area of the regular polygon:
in²
The area of the regular polygon is 374.1 in².
Answer:
390625
Step-by-step explanation:
The questions are all independent -- the answer on one question does not limit the number of possible answers on another question.
The quiz has 5 choices for each question, so there are
ways to answer the quiz questions.
Notice that this could be written 
. You could say that the number of ways to answer the questions is
Use a calculator to find
Answer:
5 and -5
Step-by-step explanation:
Opposite numbers are the same distance from 0 on the number line. So, each of the numbers is a distance from zero that is half the distance between them.
The numbers are 10/2 = 5, and -5.
