Step-by-step explanation:
R' = (-2,0)
E' = (-2,2)
F' = (4,4)
To find w, you subtract 117 from 180. After that you get w = 63. Now you add 63 and 31 to get 94. You then subtract 94 from 180 to get x = 86. Now you add 86 and 56 to get 142. You then subtract 142 from 180 to get y = 38. Now you add 38 and 117 to get 155. Again you subtract 155 from 180 to get z = 25
Answer: s = 36
Step-by-step explanation: The key to solving multistep equations is isolating the variable. This is why I first subtracted 14 on each side. This left me with 1/3s=12. Then, to isolate "s" even more, I didvided by 1/3 on each side. This gave me s = 36 as an answer.
To divide by a fraction, use "keep change flip." Keep the first mumber, change division to multiplication, and flip the fraction. I included a picture of me doing this.
If you have any other questions, please feel free to ask :)
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: option d. the argument is valid by the law of detachment.
The law of detachment consists in make a conlcusion in this way:
Premise 1) a => b
Premise 2) a is true
Conclusion: Then, b is true
Note: the order of the premises 1 and 2 does not modifiy the argument.
IN this case:
Premise 1) angle > 90 => obtuse
Premise 2) angle = 102 [i.e. it is true that angle > 90]]
Conclusion: it is true that angle is obtuse
