Show Work and explain but quickly, please.

1 answer:

4 0

Answer:

Z= -4.6

Step-by-step explanation:

z/2-3/5=2/3z +6

you first find the LCM of both sides

LCM of 5 and 2 is 10 then LCM of 3 and 6 is 6

5z-6/10 = 4z+1/6

then you cross multiply

6(5z-6)=10(4z+1)

open the bracket

30z-36=40z+10

collect like terms

30z-40z=36+10

-10z=46

z= -46/10

= -4.6

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ryzh [129]

Could you translate it?

4 0

3 years ago

seraphim [82]

Answer:

$y=\frac{x}{2}+\frac{2}{3}$

Step-by-step explanation:

The inverse function $f^{-1}$ of a function $f$ must meet that if $f(a)=b$ , then $f^{-1}(b)=a$ .
To find the inverse function one can clear out x from the initial equation, and once obtained an expression x=f(y), replace x by y, where y=f(x).
In this case, $y=h(x)=2x-\frac{4}{3}$ .
To find the inverse function, we clear out x, as follows: $y=2x-\frac{4}{3}$ ⇒ $y+\frac{4}{3} =2x$ ⇒ $x=\frac{y}{2}+\frac{2}{3}$ .
Now that we have clear out the value of x as a function of y, we just have to replace x by y: $y=\frac{x}{2}+\frac{2}{3}$ , which is the inverse function we have been looking for.

To corroborate the function is correct, we can use the fact that $f(a)=b$ , then $f^{-1}(b)=a$ . If we take x=1, in the first equation $f(1)=2-\frac{4}{3} = \frac{2}{3}$ . If now we replace b=2/3 in the inverse function we obtain $f^{-1}(\frac{2}{3})=\frac{\frac{2}{3} }{2} +\frac{2}{3} =1$