Answer:
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Step-by-step explanation:
Let
x -----> represent the measures of the seven same-size angles,
x/2 ----> represent the measure of the one that is "two times smaller."
we know that
The sum of internal angles of a polygon can be calculated as:
where
n is the number of sides of the polygon
In this case
n=8 (octagon)
substitute
so
The linear equation that represent this problem is
solve for x
so
therefore
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Answer:
3 and 28
Step-by-step explanation:
note (
)(x ) = 
= 
and
( )(4) = 
= 
= 
= 3
-------------------------------------------------------
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= x² + 2x - 3 + x² - 9 = 2x² + 2x - 12 and
(f + g)(4) = 2(4)² + 2(4) - 12 = 2(16) + 8 - 12 = 32 + 8 - 12 = 28
Answer:
14/45
Step-by-step explanation:
So we have the fraction:
We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:
Since there is only 1 digit repeating, let's multiply everything by 10. So:
Now, subtract n from both sides:
On the left, substitute the number for n. On the right, combine like terms:
All of the 1s will cancel. So:
Subtract:
Divide both sides by 9:
Remove the decimal by multiplying both sides by 10:
Reduce:
And we're done!
Use a calculator to check:
Answer:
The population will be 240,116
Step-by-step explanation:
Exponential growth can be represented by the expression:
where:
is the population at time (t)
is the initial value of the population
"r" is the annual rate of growth (written in decimal form)
and "t" is the time in years.
Therefore in this situation, P(16) is what we want to find [the population after 16 years]
the initial population is 110,000
the rate of growth is 0.05 [decimal form of 5%]
and t is 16 years.
Replacing all these in the given functional form gives:
