Explanation:
For a quadratic equation in standard form with real coefficients:

The quadratic formula giving its solutions is ...

The quantity under the radical is called the discriminant. If we let d represent it, then ...
d = b²-4ac
and there are three possibilities:
- d < 0. The solutions involve the square root of a negative number, so both are complex. They are conjugates of each other.
- d = 0. There is one real solution. It has multiplicity 2.
- d > 0. There are two distinct real roots.
If the coefficients of the quadratic are rational, the roots will be irrational if and only if d is not a perfect square.
_____
The above formula still applies when coefficients are complex or irrational (or both). In the case of complex coefficients, the description of the number of roots is accurate, but their description as real or complex may not apply.
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<u>Examples</u>:
(x -1)² +1 = 0 = x² -2x +2 . . . . d = (-2)²-4(1)(2) = -4; roots are x = 1 ± i
(x-2)² = 0 = x² -4x +4 . . . . . . d = (-4)² -4(1)(4) = 0; roots are x = 2 (twice)
(x+3)² -4 = x² +6x +5 . . . . . . d = 6² -4(1)(5) = 16; roots are x = -5 and x = -1
Answer:
9units
Step-by-step explanation:
Answer:
Quadrant 2
Step-by-step explanation:
First you reflect and it goes to Quadrant 4(Positive,Negative). When rotating 90 degrees you go to the next quadrant. In this case it is 180 degrees, so it ends up two quadrants away. The final location is quadrant 2
Answer:
Area of the shaded area = 60 m^2
Step-by-step explanation:
Remark
I don't think you need the 40 degrees for anything.
Formula
Area of Shaded part = area of the rectangle - area of the triangle
Solution
<u>Area of the Rectangle</u>
L = 12 meters
W = 10 meters
Area = 12 * 10
Area = 120 m^2
<u>Area of the triangle</u>
Area = 1/2 b * h
b = 12
h = 10
Area = 1/2 * 12 * 10
Area = 120/2 = 60
Area of the shaded area
120 - 60 = 60
He has used to much money I think but still is if he uses he will have 752 and then he will not have the amount that he needs.