10. A 11. D 12. A (wasn’t too sure about question 12)
17.5 is bigger.1\6 is small.
Answer:
Put the equation in standard form by bringing the 4x + 1 to the left side.
7x2 - 4x - 1 = 0
We use the discriminant to determine the nature of the roots of a quadratic equation. The discriminant is the expression underneath the radical in the quadratic formula: b2 - 4ac.
b2 - 4ac In this case, a = 7, b = -4, and c = -1
(-4)2 - 4(7)(-1)
16 + 28 = 44
Now here are the rules for determining the nature of the roots:
(1) If the discriminant = 0, then there is one real root (this omits the ± from the quadratic formula, leaving only one possible solution)
(2) If the discriminant > 0, then there are two real roots (this keeps the ±, giving you two solutions)
(3) If the discriminant < 0, then there are two imaginary roots (this means there is a negative under the radical, making the solutions imaginary)
44 > 0, so there are two real roots
I hope you can see it just try to zoom in
The probability of an event is expressed as
Given:
The probability of drwing two blue balls one after the other is expressed as
For the first draw:
For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
The probability of drawing two blue balls one after the other is evaluted as
The probablity that none of the balls drawn is blue is evaluted as
Hence, the probablity that none of the balls drawn is blue is evaluted as
