Answer:
Tn = 4(-6)^n-1
Step-by-step explanation:
Write an explicit formula for an, the nth term of the sequence 4, -24, 144, ....
The sequence is a geometric sequence
Tn = ar^n-1
a is the first term
a = 4
r = -24/4 =144/-24
r = -6
Substitute
Tn = 4(-6)^n-1
Yea yea :8+10 and we paid for the roaches
Let x be the number of days.
Daily pass:
65x + 30x
95x
Season pass:
400 + 30x
95x > 400 + 30x
65x > 400
x > 6.15
The number of days can't be 6.15, so you must round. You can't go down because then the price will be more expensive, so you have to round up.
It would take 7 days until the season pass is less expensive than the daily pass.
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You can check this by plugging in the x.
95x > 400 + 30x
95(7) > 400 + 30(7)
665 > 400 + 210
665 > 600
The daily pass is more expensive than the season pass.
Since we have two possible pieces of information and 2 items to solve for, we know this is a system of equations.
Our first piece of information is that our shorter leg (s) is 2 feet shorter than our longer leg (l). This can be written as s=l-2.
Our second piece of information is that using the Pythagorean theorem that our shorter leg squared plus our longer leg squared is equal to our hypotenuse squared. This can be represented by s^2+l^2=10^2. Now we can solve.
We have already isolated for s in our first equation, so we can substitute l-2 in.
(l-2)^2+l^2=10^2
l-2+l=10
2l-2=10
2l=12
l=6
Now we can substitute in for s in our simpler equation
s=6-2
s=4
We now know that using our knowledge of systems of equations, the side lengths of this right angle triangle are 6 and 4.
The domain is the complete set of values for which x, or the independent variable, is possible for.
The range is the complete set of values for which y or the dependent variable is possible for.
Hope this helps.
