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love history [14]
3 years ago
13

Use f(x)=3x/x+1 and g(x)=-2/x+1 to find the following

Mathematics
1 answer:
maksim [4K]3 years ago
4 0

Answer:

a) 3x-2/x+1

b)14/5 as an improper fraction or 2 and 4/5 as a mixed number

Step-by-step explanation:

a) You just have to add f(x) and g(x) together and since the denominator is the same you can just add the numerators which gives you 3x-2/x+1

b)You have to plug in 4 to every x value in both functions so you get 3(4)/4+1 for f(x) and -2/4+1 for g(x) this simplifies down to 12/5 and -2/5 you then have to subtract those two fractions as stated in part b which gives you 14/5 as an improper fraction or 2 and 4/5 as a mixed number

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\bf \qquad \qquad \textit{double proportional variation}\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\

\bf \begin{cases}
p=pedalisi\\
w=weight\\
s=\textit{sitting height}
\end{cases}\quad 
\begin{array}{llll}
%pelidisi, varies directly as the cube root of a​ person's weight in grams and inversely as the​ person's sitting height in centimeters.
\textit{pelidisi varies directly}\\
\textit{as cube root of weight}\\
\textit{and inversely to }\\
\textit{sitting height}
\end{array}\implies p=\cfrac{k\sqrt[3]{w}}{s}\\\\
-------------------------------

\bf \textit{we know that }
\begin{cases}
w=48,820\\
s=78.7\\
p=100
\end{cases}\implies 100=\cfrac{k\sqrt[3]{48820}}{78.7}
\\\\\\
100\cdot 78.7=k\sqrt[3]{48820}\implies \cfrac{7870}{\sqrt[3]{48820}}=k
\\\\\\
thus\qquad \boxed{p=\cfrac{\frac{7870}{\sqrt[3]{48820}}\sqrt[3]{w}}{s}}
\\\\\\
\textit{now, what is \underline{p} when }
\begin{cases}
w=54,688\\
s=72.6
\end{cases}?\implies p=\cfrac{\frac{7870}{\sqrt[3]{48820}}\sqrt[3]{54688}}{72.6}

now, if that value is less than 100, then the fellow is "undernourished", otherwise, is overfed.
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Step-by-step explanation:

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