Answer:
an = 115 + (n - 1) (-6)
a25 = - 29
Step-by-step explanation:
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
a5 = 91 = a1 + (5 - 1) d
91 = a1 + 4 d
a20 = 1 = a1 + (20 - 1) d = a1 + 19 d
1 = a1 + 19 d
now we subtract term by term one expression from the other
90 = 4 d - 19 d
90 = - 15 d
divide both sides by -15 to isolate d
d = 90 / (-15) = -6
Now we can calculate what a1 is using for example:
1 = a1 + 19 d
1 = a1 - 114
add 114 to both sides:
115 = a1
Then our general expression for the sequence is:
an = 115 + (n - 1) (-6)
We can now use it to calculate the value of a25:
a25 = 115 + (24) * (-6) = -29
Answer:
(x+11), (y+15)
Step-by-step explanation:
the point v gets translated 11 points to the right, so the translation is x+11.
Point v also gets translated 15 points up, so the translation is y+15
Closure for addition and multiplication.
Commutative property for addition and multiplication.
Associative property for addition and multiplication.
Distributive property of multiplication over addition.
Identity for addition and multiplication.
Hope this helps; have a great day!
Answer:
19/4
Step-by-step explanation:
0.5=12/10a-5.2
1/2=6/5a-26/5
5=12a-52
-12a=-57
Use the sine function here.
x
--- = sin 20 degrees = 0.349, so x = 10(0.349) = 3.42
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