Answer:Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8
Answer:
Step-by-step explanation:
a1 = 8
a9 = 56
Using formula for finding nth term of arithmeric sequence
We have to find 24th term, therefore n = 24
is the first term but we are missing d
d is the difference between the two consecutive terms, lets calculate it first
a9 = 56
Using the above given formula for finding d
put n = 9, a9= 56
56 = 8 + 8d
8d = 48
d = 6
Getting back to main part of finding 24th term
n = 24, d = 6, a1 = 8
put values in nth term formula
So 2 gallons every 5 minutes
2/5= .4
so .4 a minute
and you already have 5 gallons in so those need to be added
m=minutes
y=0.4m + 5 will be what you want to find out if you are looking to find out how much will be there in a certain time
for 50 minutes you will have
y=0.4(50) +5
20+5
25 gallons
HOWEVER, the equation has to be changed if you want to tell how long you have to wait for it to fill.
m=2.5(g-5)
m=minutes
g= gallons
you subtract 5 because they are already there
you multiply by 2.5 because it fills at a rate of 1 gallon every 2.5 minutes.
m=2.5(1500-5)
for the sake of it being easier i will do the -5 separately
2.5(1500 = 3750
2.5(-5= -12.5
3750-12.5
3737.5 minutes to fill the pool.
3720/60 = 62
17.5/60 = .292
62.292 hours to fill the pool.
p.s. you have a really slow hose.
Its good you didn't wait for it to fill, you would have died from lack of water before then if you just sat and waited.
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Answer:
Read the problem carefully. For the purposes of this step-by-step geometry proof, use the following example: Given that triangle ABC is an equilateral triangle and that line AD bisects line BC, prove that the resulting triangle ABD is a right triangle.Draw an illustration of the problem. Having a picture in front of you when doing a geometry proof really helps organize your thoughts.Consider what you know about each piece of given information. For example, because ABC is an equilateral triangle, all three sides must be the same length. Furthermore, all three angles must be equal as well. Since a triangle contains 180 degrees, then each angle in an equilateral triangle must measure 60 degrees. Moving on to the other piece of given information, since line AD bisects side BC, that makes line segments CD and DB equal in length.Use the facts established by the given information to generate more facts that are useful to your geometric proof. Since the line segments CD and DB are equal in length, that means the angle CAD must be equal to the angle DAB.Extrapolate from the facts to get closer to the solution. Since angle A is 60 degrees, the smaller angles must be one half of 60, or 30 degrees. Given that angle B is 60 degrees and that angle DAB is 30 degrees, this accounts for 90 degrees of a triangle. The remaining 90 degrees must be contained in the angle BDA. Since a right triangle must contain a 90-degree angle, you have just proven that triangle ABD is a right triangle.Write out the step-by-step geometric proof of the problem in a two-column format. In the left hand column, write a statement and in the right hand column, write the proof of the statement. Repeat this process until you have documented all of the steps in your thinking process that resulted in your solution.
Step-by-step explanation:
