( 6 − 7 i ) ( − 8 + 3 i )
First FOIL:
( 6 − 7 i ) ( − 8 + 3 i ) = -48 + 18i + 56i -21i^2
Combine like terms
= -48 + 74i -21i^2
Convert i^2 = -1
= -48 + 74i -21(-1)
And simplify
= -48 + 74i + 21
= -27 + 74i
Slot method
1st slot, 5 options
2nd slot, 4 options (1 gone to the first slot)
3rd slot, 3 options (1 gone again)
4th slot,2 options (1 less)
multiply
5*4*3*2=120
answer is 120 arrangements
Answer:
difference in the proportion = 0.0452
Step-by-step explanation:
x1 = 27, n1 = 193,
p1 = 27/193
p1 = 0.1399
x2 = 16, n2 = 169,
p2 = 16/169
p2 = 0.0947
a) The best estimate for the difference in the proportion of smokers, using male proportion minus female proportion is 0.0452. Male smokes more than females in given sample.
p1 - p2 = 0.1399 - 0.0947
p1 - p2 = 0.0452
The zeroes are
0, -5, 3 + i (and its conjugate)
The factors are
x (x + 5) (x - (3 + i)) (x - (3 - i))
Expanding...
(x² + 5x)((x - 3) - i) ((x - 3) + i)
(x² + 5x)((x - 3)² - i²)
(x² + 5x)(x² - 6x + 9 - (-1))
(x² + 5x)(x² - 6x + 10)
x⁴ - 6x³ + 10x² + 5x³ - 30x² + 50x
x⁴ - x³ - 20x² + 50x
Answer:
x=-2
Step-by-step explanation:
To solve this equation, we can use PEMDAS or Order of Operations.
Parenthesis
Exponents
Multiplication>Division
Addition>Subtraction
Using the various properties can also help make the equation easier.
First, solve for parenthesis using the distributive property.
Our equation is now : 3/4x+3=1/4x+2
Now, subtract 2 on both sides, to cancel out the positive 2 on the right.
3/4x+1=1/4x
Now subtract 3/4x from both sides.
1=-2/4x
Finally, to isolate x, divide both sides by -2/4
1/-2/4=-2
x=-2
Hope this helps!
