Answer:
P = 42.84 cm
Step-by-step explanation:
A half-circle is joined to an equilateral triangle with side lengths of 12 units.
We need to find the perimeter of the resulting shape.
The perimeter of the half cirle is πr.
The diameter of the circle is 12. It means radius is 6 units.
An equilateral triangle has 3 equal sides. So, perimeter of the triangle is given by :
P = πr + 12 +12
= 3.14(6) + 24
= 42.84 cm
Hence, the perimeter of the resulting shape is 42.84 cm.
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:
D) None of the above
Step-by-step explanation:
These are no supplementary or complimentary because they do not add up to 180 and to be vertical they would have to be across from each other
In order to prove this, you simply plug in the number 2 everywhere you see X:
4^(2) = 8(2).
Simplify
16 = 16 √
Since this checks out, x is proven to be 2.
