3. How many arrangements can be made using 4 letters of the word HYPERBOLAS if no letter is to be used more than
once?
A) 5,040
B) 151,200
C) 302,400
D) 210
E) None of the above

Correct A

Explanation:

A. Given that the equation x2+ mx+ n= 0 has two solutions, x = kand x = 2k,you can work backward to build the original equation. Here’s how:

x= kx= 2k

x– k= 0 x– 2k= 0

Now take the two equations and combine them:

(x– k)(x– 2k) = 0

x2– 2kx– kx + 2k2= 0

x2– 3kx + 2k2= 0

As you can see, m= –3kand n = 2k2, so mn= –6k3.

Edit: OMG, I'm so sorry. I didn't realize I answered the wrong question until after I posted it. Please let me know if there's a way to delete this as I don't know the answer.

i am sure it will be 90 degrees.

step-by-step explanation:

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )