Answer:
p = x² − 6x + 10
Step-by-step explanation:
Complex roots come in conjugate pairs. So if 3−i is a root, then 3+i is also a root.
p = (x − (3−i)) (x − (3+i))
p = x² − (3+i)x − (3−i)x + (3−i)(3+i)
p = x² − 3x − ix − 3x + ix + (9 − i²)
p = x² − 6x + 10
You can check your answer using the quadratic formula.
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ 6 ± √(36 − 40) ] / 2
x = (6 ± 2i) / 2
x = 3 ± i
Just add up the component areas- the 2 triangles, and then break the remainder into a rectangle and a triangle.
Answer:
Step-by-step explanation:
1st expression: x⁴-y⁴
= (x²)² - (y²)²
= (x² +y²)(x² -y²)
= (x² +y²)(x +y)(x -y)
= (x +y)(x -y)(x² +y²)
2nd expression: x² -y²
= (x +y)(x -y)
3rd expression: x³ -y³
= (x -y)(x² +xy +y²)
Now ,
Lowest Common Multiples (L.C.M.) = common factors * rest factors
= (x+y)(x-y) * (x² +y²)(x² +xy +y²)
= (x² -y²)(x²+y²) * (x² +xy +y²)
= (x⁴ -y⁴)(x² +xy +y²)
Answer:
a). x + y + 90° = 180°
b). x = 67°
y = 23°
Step-by-step explanation:
The sum of all angles in a triangle is 180°.
One of the angles in the figure is a right angle, or 90°. Therefore the sum of the three angles in the figure is:
x + y + 90 = 180
We are also told that x + 2 = 3y.
Rearranging that to isolate x gives us:
x = 3y - 2
Thake the first equation and substitute the above expression of in place of x:
x + y + 90° = 180°
(3y-2) + y + 90° = 180°
4y + 88° = 180°
4 y = 92°
y = 23°
To find angle x, use y = 23°
x = 3y - 2
x = 3*(23°) - 2
x = 67°
The sum 90° + 67° + 23° = 180°
Answer:
-3g
Step-by-step explanation:
