We have an arithmetic progression:
an=number of item at row n
an=a₁+(n-1)d
d=common difference=an-a(n-1)=a₂-a₁=2-1=1
n=number of row
In this case:
an=1+(n-1)*1=n
The sum of an arithmetic serie is:
Sn=(a₁+an)n / 2
In this case:
a₁=1 (number of itms in the first row)
an=n (we have to calculate this before)
Sn=(1+n)n /2=(n+n²)/2
Therefore:
f(n)=Sn=number of items when we have n number of rows
f(n)=(n+n²)/2
Answer: f(n)=(n+n²)/2
To chek:
f(1)=(1+1²)/2=1
f(2)=(2+2²)/2=6/2=3
f(3)=(3+3²)/2=(3+9)/2=12/2=6
....
Question:
A camel can drink 25 gallons of water in 10 minutes. How many cups of water can the camel drink in 10 minutes?
Solution:
A)
1 cup = 0.25 quarts.
4 quarts= 1 gallon
Then, according to this information, we get the following table:
B)
Note that 4 quarts= 1 gallon, then 1 gallon is equivalent to 16 cups.
C)
Then, 25 gallons are equivalent to:
D. According to the above information, we obtain that 25 gallons of water are 400 cups .
So that, we can conclude that the correct answer is:
The camel can drink 400 cups of water in 10 minutes
To do this problem you need to find angle adc which is a part of angle BDA. angle BDA is 90 degrees so the 2 parts must add up to 90 degrees so you set up the problem like this
-2x + 144 - 3x +51 =90
then you combine like terms
-5x +195 = 90
then you subtract 195 from 90
-5x = -105
then you divide -5 by -5 and -105 by -5 and get
x=21
then you plug x in and get your angle measure
-3(21) +51
then you get the angle measure as 114 degrees.
Answer:
Step-by-step explanation:
Use substitution, y=3x+18 so -12x+4(3x+18)=-24. From here you can try to solve for x
-12x+12x+72=-24
The xs cancel, which leaves you with 72=-24
Since 72 cannot equal -24 there is no answer to this system of equations
