Find the value for this expression if a= -2, c = 2 and z = -4.2:

−4|c−3|+2|z−a|

If x/b+c=y/c+a=z/a+b, then how do you prove that (b-c) x+(c-a) y+(a-b) z=0?

Write xb+c=yc+a=za+b=k.

Sort of “unreducing” each fraction in a useful manner, we could write

x(b−c)(b+c)(b−c)=y(c−a)(c+a)(c−a)=z(a−b)(a+b)(a−b)=k.

Componendo-Dividendo says that the fraction formed by the sum of the tops over the sum of the bottoms is still equal to k. That is

(b−c)x+(c−a)y+(a−b)zb2−c2+c2−a2+a2−b2=k.

Therefore,

(b−c)x+(c−a)y+(a−b)z=k(b2−c2+c2−a2+a2−b2)

and so

(b−c)x+(c−a)y+(a−b)z=0

Quick, smart and stylish.

Since all the terms are equal it must be equal to some constant value. So say

x/(b+c) = y/(c+a) = z/(a+b) =p

equating separately we get

x=p(b+c)

y=p(c+a)

z=p(a+b)

Now consider the equation

(b-c)x+(c-a)y+(a-b)z=k

k=p(b-c)(b+c)+p(c-a)(c+a)+p(a-b)(a+b)

k=p(b²-c²+c²-a²+a²-b²)

k=p(0)

k=0

So as considered

(b-c)x +(c-a)y+(a-b)z=0

Step-by-step explanation:

i think it is x = 1.2

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: