Answer:
BD = 6
Step-by-step explanation:
Theorem: The altitude to the hypotenuse of a right triangle is the mean proportional between the segments of the hypotenuse.
So, 

BD = 6
See how easy that is IF you know the theorem.
Answer:
I would change 2x+4y=24 into x=12–2y
To do that, divide both sides by 2 and then subtract 2y on each side.
After that, substitute for x. 3x+2y=19 would become 3(12–2y)+2y=19.
Then solve.
3(12–2y)+2y=19
36–6y+2y=19
-4y+36=19
-4y=-17
y=4.25
Then, substitute y in either equation.
Either this:
3x+2y=19
3x+2(4.25)=19
3x+8.5=19
3x=10.5
x=3.5
Or:
2x+4y=24
2x+4(4.25)=24
2x+17=24
2x=7
x=3.5
Or you could solve it in the equation you created in the beginning:
x=12–2y
x=12–2(4.25)
x=12–8.5
x=3.5
The coordinates where the lines intercept are (3.5, 4.25).
Sorry for the long answer!
Answer:
Step-by-step explanation:
(a - b)(a +b) = a² - b²
1 - Sin² A = Cos² A

2) Sec² A - Tan² A = 1

3) LHS = Cosec² A + Cot² A
= Cosec² A + Cosec² A - 1
= 2Cosec² A - 1 = RHS

Answer:
2(3x+6) = 6x+12
3(2x-6) = 6x-18
6x+12=6x-18
Subtract 12 from 18, which gives you:
6x=6x-6
Subtract the 6x on the opposite side of the equal side, and your answer is: x = -6