Answer: a) An = An-1 + An-2
b) 55ways
Step-by-step explanation:
a) a nickel is 5 cents and a dime is 10cent so a multiple of 5 cents is the possible way to pay the tolls in both choices.
Let An represents the number of possible ways the driver can pay a toll of 5n cents, so that
An = 5n cents
Case 1: Using a nickel for payment which is 5 cents, the number of ways given as;
An-1 = 5( n-1)
Case 2: using a dime which is two 5 cents, the number of ways is given as;
An-2 = 5(n-2)
Summing up the number of ways, we have
An = An-1 + An-2
From the relation,
If n= 0, Ao= 1
n =1, A1= 1
b) 45 cents paid in multiples of 5cents will give us 9 ways(A9)
From the relation, we have that
Ao = 1
A1 = 1
An =An-1 + An-2
Ao = 1
A1 = 1
A2 = A1+Ao = 1+1= 2
A3 = A2 + A1 = 3
A4 = A3+A2=5
A5=A4+A3=8
A6=A5+A4=13
A7 =A6+A5 = 21
A8= A7+A6= 34
A9= A8+A7= 55
So there are 55ways to pay 45cents.
Answer:
n = 19.89694
Step-by-step explanation:
You can work the problem using decimal numbers. There is no need to convert everything to integers. Trying to do so just gets you in trouble.
Subtract 2.2 from both sides:
-1.398 -2.200 = n/-5.53
-3.598 = n/-5.53
Now, multiply both sides by -5.53:
(-5.53)(-3.598) = n = 19.89694
_____
The one rule that cannot be violated in algebra is that <em>you must do the same thing to both sides of the equation</em>.
_____
Your "solution" so far has a couple of errors. The first is that you have apparently multiplied all of the numbers by 1000. Unfortunately, when you multiply a denominator by 1000, it is the same as dividing by 1000. So, you have multiplied the left side by 1000, multiplied one term on the right by 1000 and divided another term on the right by 1000. This turns the equation into something different than what you started with, and will give a wrong answer.
The second error is that you have subtracted 2200 only from the right side. This, too, will turn the equation into something different than what you started with, and will give a wrong answer.
Answer:
Step-by-step explanation:
hello :
an equation of this graph is : f(x) = a(x-h)²+k when (h,k) the vertex
so : h=5 and k= -4
f(x) = a(x-5)²-4....... now calculate : a
the y- intercept is : - 6.5 means : f(0) = - 6.5
put x=0 and f(x) = - 6.5
you have : -6.5 = a(0-5)²-4
-6.5 = 25a - 4
25a = -2.5 so : a= -2.5/25= 1/10
the equation is :
<h2>f(x) = (1/10)(x-5)²-4</h2>
Answer:
1 and -8
Step-by-step explanation:
Answer:
The required equation is 6x+5y+57=0.
