The quadratic formula is =(-b+-sqrt(b^2-4ac))/2a
as you notice the term under the square root is b^2-4ac if it is postive then the equation clearly will have two real soultions if it is negative then the equation will have two imaginary soultion if it is zero then the the equation will have one soultion
so let us calculate b^2-4ac for our given equation
x^2=4x-5 so let us write it in general form which is ax^2+bx+c=0
subtracting 4x from both sides
x^2-4x=-5
adding 5 to both sides
x^2-4x+5=0
a=1,b=-4,c=5
b^2-4ac=(-4)^2-4(1)(5)=16-20=-4
which means the equation has two imaginary soultions
Total number of marbles=5+3+4=12
Probability of picking a red marble =5/12
1.) a>10
2.) a<3.5
How I got it: 1.) Subtract 3 from both sides, leaving -2a<10.
2.) Divide by -2 from both sides, remember to flip the inequality sign when dealing with negatives. This leaves you with a>10.
For number 2.) I divided both sides by 5, leaving a<3.5, though this answer may be wrong.
0.9 is 0.9278 rounded to the nearest tenth. Hope this helps!
A^2 + b^2 = c^2
12^2 + 17^2 = 485
so c^2=485
so c=22.0 inches
