0.04 gallons per mile
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The sum of any arithmetic sequence is the average of the first and last terms times the number of terms.
Any term in an arithmetic sequence is:
a(n)=a+d(n-1), where a=initial term, d=common difference, n=term number
So the first term is a, and the last term is a+d(n-1) so the sum can be expressed as:
s(n)(a+a+d(n-1))(n/2)
s(n)=(2a+dn-d)(n/2)
s(n)=(2an+dn^2-dn)/2
However we need to know how many terms are in the sequence.
a(n)=a+d(n-1), and we know a=3 and d=2 and a(n)=21 so
21=3+2(n-1)
18=2(n-1)
9=n-1
10=n so there are 10 terms in the sequence.
s(n)=(2an+dn^2-dn)/2, becomes, a=3, d=2, n=10
s(10)=(2*3*10+2*10^2-2*10)/2
s(10)=(60+200-20)/2
s(10)=240/2
s(10)=120
Question:
Solution:
Let the function
![y=f(x)\text{ = }\sqrt[]{x}-9](https://tex.z-dn.net/?f=y%3Df%28x%29%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7Bx%7D-9)
Now remember the following rule:
To graph y = f(cx)
if 0 < c < 1 , stretch the graph of y = f(x) horizontally by a factor of 1/c.
Thus, applying this to the given function, with c = 3, we can conclude that the correct answer is:
![y=f(x)\text{ = }\sqrt[]{\frac{1}{3}x}-9](https://tex.z-dn.net/?f=y%3Df%28x%29%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B%5Cfrac%7B1%7D%7B3%7Dx%7D-9)
Let the prices of a pack of potato chips and can of coke be x and y respectively
3x+2y=50-9
3x+2y=41........... (1)
4x+5y=50+21
4x+5y=71............(2)
Multiply (1) with 4 and (2) with3
12x+8y=164
12x+15y=213
On subtracting above eqs. we get
7y= 49
y=7
Putting value of y in (2)
4x+5(7)=71
4x+35=71
4x=36
x=9
x=$9
y=$7
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