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.
If he travels 12km/h for 3 hours then he went 36km in 3hr. The answer is 36km.
2√3 ∙ 3√2= 6√6
alternate form- 14.69
rounded part is a semicircle so the area for that is the area of a circle ÷ 2
so
area of the rectangle + (area of the circle ÷ 2) = answer
24 * 14 = 336 = area of the rectangle
14 ÷ 2 = r
(pi * 7^2) ÷ 2
(pi * 49) ÷ 2 = 153.86 ÷ 2 = 76.93 = area of semicircle
336 + 76.93 = 412.93 ft^2 = answer
a) x=4
10+2x+6=24
-2x. -2x
10+6=-2x+24
-24. -24
10+6-24=-2x
simplify
-8=-2x
divide both sides by -2
4=x
2. x=7
14+3x+5=40
-3x. -3x
14+5=40-3x
-40. -40
14+5-40=-3x
-21=-3x
divide both side by -3
7=x
