How can the associative, commutative, and distributive properties be applied when performing operations on complex numbers and polynomials?

Answer with explanation:

Complex Numbers

For,any two or more complex numbers , ,

1. Commutative Property

2. Associative Property

3.Distributive Property

Hence Complex number follows ,Associative, Commutative, and Distributive Property.

Polynomials ⇒

P=a x +b, Q=c x²+ t x+d, R=m x³+ n x²+ r x+s

1. Commutative Property

P+Q=a x+b+c x²+ t x+d

      =c x²+ t x+d+a x+b

    =Q+P

2. Associative Property

(P+Q)+R=(a x+b+c x²+ t x+d)+m x³+ n x²+ r x+s

   =a x+b+(c x²+ t x+d+m x³+ n x²+ r x+s)

    = P + (Q+R)

3.Distributive Property

P×(Q+R)

  (ax+b)×[c x²+ t x+d+m x³+ n x²+ r x+s]

=(ax+b)×[c x²+ t x+d]+(ax+b)[m x³+ n x²+ r x+s]

=P ×Q+P×R

Hence Polynomial follows ,Associative, Commutative, and Distributive Property.

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation:

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.