Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
X-int =(-3,0)
Y-int=(0,_1)
Slope: _1/3
One pound is about 0.5, so pretty much divide it by half
Answer: n= -1/2
Step-by-step explanation:
Answer:
D) cot(C) = 1/2.
Step-by-step explanation:
We can go through each choice and examine is validity.
Choice A)
We have:

Recall that secant is the ratio of the hypotenuse to the adjacent.
With respect to B, the adjacent is 6 and the hypotenuse is 7.
Therefore, sec(B) should be 7/6 instead.
A is incorrect.
Choice B)
We have:

Cotangent is the ratio of the adjacent side to the opposite.
With respect to B, the adjacent side is 6 and the opposite side is 3.
Therefore, cot(B) = 6/3 = 2.
B is incorrect.
Choice C)
C is incorrect for the reasons listed in A.
Choice D)
We have:

Again, cotangent is the ratio of the adjacent side to the opposite.
With respect to C, the adjacent side is 3 and the opposite side is 6.
So, cot(C) = 3/6 = 1/2.
Therefore, D is the correct choice!