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lukranit [14]
2 years ago
7

Need help please thank you

Mathematics
1 answer:
svetoff [14.1K]2 years ago
4 0

Answer:

  D.  x = -7/3

Step-by-step explanation:

A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.

<h3>F(x) = 0</h3>

The desired form can be found by subtracting 16 from both sides of the equation:

  \left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16

A graph is attached, showing x=-7/3 is the solution.

<h3>Algebraic solution</h3>

Using powers of 4, the equation can be rewritten ...

  \left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}

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Answer:

Step-by-step explanation:

P = 4x(x - 3) + 4y(y - 3) + 8xy

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x+y =2 ⇒ P = 4.2² - 12.2 = 16 - 24 = -8

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Answer:

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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3. Solving the system by Elimination

\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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3 years ago
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The total of 2 buckets of popcorn and 3 boxes of candy would be $23.25

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There are then two possible ways to solve; you can either say that C = 9.75 - P using the second equation and then substitute it into the first, or you can multiply the second equation by either 4 or 6 to cancel out P or C.

I’m going to multiply the second equation by 4:

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Now we can substitute this value of C into one of the equations to find P:

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And now to answer the question, you just multiply P by 2 and C by 3 and add them together, which gives you $23.25

I hope this helps! Let me know if you have any questions :)

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Step-by-step explanation:

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