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BartSMP [9]
3 years ago
15

An artist purchased 24 high quality canvases to be used for painting this fall. Each week she will allow herself to use three of

the canvases for painting until all 24 canvases have been used.
Write a linear equation modelling the number of canvases remaining (y) as a function of weeks painting (x).
Mathematics
1 answer:
Nadusha1986 [10]3 years ago
8 0

Answer:

<u><em>canvases over weeks </em></u>

<u><em> </em></u>

<u><em>Step-by-step explanation: </em></u>

<u><em> </em></u>

<u><em>Given: </em></u>

<u><em> </em></u>

<u><em>w(h) represents how many hours per week </em></u>

<u><em> </em></u>

<u><em>c(t) approximates how many canvases she paints per hour </em></u>

<u><em> </em></u>

<u><em>In function composition, if we have two function f(x) and g(x) then </em></u>

<u><em> </em></u>

<u><em>(f.g)(x) or f(g(x)) means first apply g(), then apply f() i.e. applying function f to the results of function g. </em></u>

<u><em> </em></u>

<u><em>Now we have c(w(h)), this means first we apply w(h) which will give us hours per week and then we'll apply function 'c' on the results of 'w' (that is number of hours for weeks painted). As result we'll get number of canvas </em></u>per week!

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1) X stands for individual acts and y,  group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) S=\left \{ 5,10 \right \}

Step-by-step explanation:

Completing with what was found:

<em> 1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30</em>

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Besides that, In the system of equation, they represent the time for x, and the time for y.

2. Do you agree that your classmate set up the equations correctly? Explain why or why not.

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\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}

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