Answer:
exterior angles:
144°and 36°
126° and 54°
90° and 90°
Step-by-step explanation:
we know that each angle in a triangle adds up to 180°.
so,
2x+3x+5x=180
10x=180
x=180/10
x=18
the interior angles are:
2x=36°
3x=54°
5x=90°
and explanation is provided to find the exterior angles above.(sorry for the bad handwriting)
With 
and 
, we have
Then 
has critical points where
where 
is any integer.
is increasing wherever 
, which happens for
Answer:
1. x=60
2.x=5
3.x=8
4.x=10
Step-by-step explanation:
im assuming you want to find x value for each.
<em /><u><em /></u>I think that both lines will show only 1 line because 1 line will be on top of the other. I believe this because both lines are dilated with its center at point O which does not lie on line n. Whatever dilation Andre uses may also be the dilation used by Becca since their lines centered at point O. Both lines will have the same slope and share the same coordinates.
Part A
Answer: The common ratio is -2
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Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
-----------------------------------
Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
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Part C
Answer: The next three terms are 16, -32, 64
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Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
