Answer:
Option D
Step-by-step explanation:
Cos M =
Cos M =
Its is true that C ⊆ D means Every element of C is present in D
According to he question,
Let C = {n ∈ Z | n = 6r – 5 for some integer r}
D = {m ∈ Z | m = 3s + 1 for some integer s}
We have to prove : C ⊆ D
Proof : Let n ∈ C
Then there exists an integer r such that:
n = 6r - 5
Since -5 = -6 + 1
=> n = 6r - 6 + 1
Using distributive property,
=> n = 3(2r - 2) +1
Since , 2 and r are the integers , their product 2r is also an integer and the difference 2r - 2 is also an integer then
Let s = 2r - 2
Then, m = 3r + 1 with r some integer and thus m ∈ D
Since , every element of C is also an element of D
Hence , C ⊆ D proved !
Similarly, you have to prove D ⊆ C
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Answer:
The measure of the angle is 36°
Step-by-step explanation:
Let the measure of angle be x
Supplementary angles : A pair of angles whose sum is 180° is called supplementary angles
So, Supplement of x = 180°-x°
Complementary angles A pair of angles whose sum is 90° is called complementary angles
So, Complement of x = 90°-x°
We are given that Three times the measure of a supplement of an angle is eight times the measure of a complement of the angle
So, 3(180-x)=8(90-x)
540-3x=720-8x
8x-3x=720-540
5x=180
x=36
So, the measure of the angle is 36°
Answer:
FCB is a better deal because you have to pay less interest overall. ($1125 compared to $1575)
Step-by-step explanation:
Use this formula to solve. FV = PV(1+i)^n
FV = Future Value
PV = Present Value
i = interest in decimal form
n = number of years
FCB: FV=7500(1.15)^1 = 8625
FSL: FV=7500(1.1)^2 = 9075
Using Pythagorean thereon