Answer:
3
Step-by-step explanation:
the mean is 103, as a result you must find the distance.
from 100 to 103 is 3
from 194 to 103 is 1
from 107 to 103 is 4
Then find the mean again youll get 18/6 which is 3
X² <span>+ 11x + 7
because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:
(-b </span>± √((b)² - 4ac))/(2a)
in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))
not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2
and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:
(x - (-11 - √93)/2) and (x + (-11 - √93)/2)
they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:
(x + (11 + √93)/2) (x - (11 - √93)/2)
and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
Answer:
C. 101 - 5(n - 1)
Step-by-step explanation:
d = (26 - 71)/(16 - 7)
d = -45/9
d = -5
a7 = a1 + (7-1)(-5)
71 = a1 - 30
a1 = 101
an = 101 + (n - 1)(-5)
an = 101 - 5(n - 1)
Given that
and
, if
is an arithmetic sequence, then the common difference between successive terms is
.
You then have
So the explicit formula for the
th term is
