Answer:
<h2>
m∠a = 67° , m∠b = 42°</h2>
Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
The term "closed" in math means that if you take two items from a set, do some operation, then you'll always get another value in the same set (sometimes you may get the same value as used before). For example, adding two whole numbers leads to another whole number. We therefore say "the set of whole numbers is closed under addition". This applies to integers as well because integers are positive and negative whole numbers. So we can say that integers are closed under addition.
Integers are not closed under division. Take two integers like 2 an 5 and divide: 2/5 = 0.4 which is not an integer. Integers don't have decimal parts.
The set of whole numbers is {0,1,2,3,...} and we can subtract the two values 1 and 2 to get 1-2 = -1. The order matters here. Subtracting a larger value from a smaller leads to a negative. The value -1 is not in the set of whole numbers. So we can say that whole numbers is not closed under subtraction
Finally, the set of irrational numbers is closed under addition. Adding any two irrational numbers leads to another irrational number. For instance, pi+sqrt(2) = 3.142 + 1.414 = 4.556; I'm using rounded decimals as approximate values. An irrational number is one where we cannot write it as a fraction of integers. Contrast that with a rational number in which we can write it as a fraction of integers. Example: 10 = 10/1 is a rational number.
A) c=18
0.5c^2 +13=94
subtract 13 from both sides
0.5c^2 = 81
Square root of both sides to get c alone
0.5c=9
double c to make it just c
c=18
B) x=8
(x-2)^2+1=37
Subtract one from each side
(x-2)^2=36
square root each side
x-2=6
add the 2 over
x=8
Answer: 52.77876 in
Explanation: C=2πr=2·π·8.4≈52.77876 in
Answer:
B) 9
Step-by-step explanation:
110 + 75 + 11x - 9 + 8x + 13 = 360
19x + 189 = 360
19x (+ 189 - 189) = 360 - 189
19x = 171
19x/19 = 171/19
x = 9
