All 3 angles have to add up to be 180 so the answer would be 90
12 cm, use the pythagorean theorem: a^2+b^2=c^2
5^2+b^2=13^2
25+b^2=169
b^2=144
b=12
12 cm
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:
No, she doesn't have enough varnish for all the floors.
Step-by-step explanation:
Area of the floor, A= 10x6-5x2=50 
Since 5 m^2 required 1 liter of varnish.
So, the amount of varnish required for 1 = 1/5= 0.2 liters.
The amount of varnish required for 50 = 0.2X50=10 liters.
Now, as 1 tin has 2.5 liters of varnish.
So, the total amount of varnish available = 3x2.5=7.5 liters, which is less than the total requirement.
Hence, she doesn't have enough varnish for all the floors.
Answer:
the desired equation is 4x - y = -10
Step-by-step explanation:
Recall that parallel lines have the same slope.
A quick trick for finding this new equation is to adapt the given equation 4x - y = 2. Replace that constant 2 with the constant C, and substitute -2 for x and 3 for y:
Our 4x - y = 2 becomes 4(-2) - (2) = C, and -8 -2 = C, or C = -10.
Then the desired equation is 4x - y = -10
