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Helga [31]
2 years ago
14

Los boletos de entrada a un juego de baloncesto para 2 adultos y 3 niños cuestan $67 y para 3 adultos y 2 niños $78. ¿Cuál es el

precio del boleto del adulto?
Mathematics
1 answer:
kap26 [50]2 years ago
3 0

The price of the adult ticket to a basketball game is $20.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

  • STEP 1 - Convert the text of problem in system of equations

                     2a+3n=67

                    3a+2n=78

where: a= adultos and n =niños

  • STEP 2 - Find the variables a and n.

                                 \begin{bmatrix}2a+3n=67\;\; equation1\\\ 3a+2n=78\;\; equation2\end{bmatrix}\\ \\ \\ \begin{bmatrix}2a+3n=67\; *(-3)\\ 3a+2n=78\; *(2)\end{bmatrix}\\ \\ \\ \begin{bmatrix}-6a-9n=-201\\ 6a+4n=156\end{bmatrix}\\ \\ \\ Sum\; of\; equations\\ \\ -6a-9n+6a+4n=-201+156\\ -9n+4n=-201+156\\ -5n=-45\\ n=\frac{-45}{-5} =9\\\\\\  Replacing\; n\; in\; equation 1\\\\2a+3*9=67\\ 2a+27=67\\ 2a=67-27\\ 2a=40\\ a=20

Thus, a=20 and n=9.

Learn more about the system of equations here:

brainly.com/question/384631

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Help!! 50 points and brainliest!
Viktor [21]

Answer:

Second choice:

x=2t

y=4t^2+4t-3

Fifth choice:

x=t+1

y=t^2+4t

Step-by-step explanation:

Let's look at choice 1.

x=t+1

y=t^2+2t

I'm going to subtract 1 on both sides for the first equation giving me x-1=t. I will replace the t in the second equation with this substitution from equation 1.

y=(x-1)^2+2(x-1)

Expand using the distributive property and the identity (u+v)^2=u^2+2uv+v^2:

y=(x^2-2x+1)+(2x-2)

y=x^2+(-2x+2x)+(1-2)

y=x^2+0+-1

y=x^2

So this not the desired result.

Let's look at choice 2.

x=2t

y=4t^2+4t-3

Solve the first equation for t by dividing both sides by 2:

t=\frac{x}{2}.

Let's plug this into equation 2:

y=4(\frac{x}{2})^2+4(\frac{x}{2})-3

y=4(\frac{x^2}{4})+2x-3

y=x^2+2x-3

This is the desired result.

Choice 3:

x=t-3

y=t^2+2t

Solve the first equation for t by adding 3 on both sides:

x+3=t.

Plug into second equation:

y=(x+3)^2+2(x+3)

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

y=(x^2+6x+9)+(2x+6)

y=(x^2)+(6x+2x)+(9+6)

y=x^2+8x+15

Not the desired result.

Choice 4:

x=t^2

y=2t-3

I'm going to solve the bottom equation for t since I don't want to deal with square roots.

Add 3 on both sides:

y+3=2t

Divide both sides by 2:

\frac{y+3}{2}=t

Plug into equation 1:

x=(\frac{y+3}{2})^2

This is not the desired result because the y variable will be squared now instead of the x variable.

Choice 5:

x=t+1

y=t^2+4t

Solve the first equation for t by subtracting 1 on both sides:

x-1=t.

Plug into equation 2:

y=(x-1)^2+4(x-1)

Distribute and use the binomial square identity used earlier:

y=(x^2-2x+1)+(4x-4)

y=(x^2)+(-2x+4x)+(1-4)

y=x^2+2x+-3

y=x^2+2x-3.

This is the desired result.

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3 years ago
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Step-by-step explanation:

steps are in picture above.

<u>N</u><u>o</u><u>t</u><u>e</u><u>:</u><u>i</u><u>f</u><u> </u><u>y</u><u>o</u><u>u</u><u> </u><u>n</u><u>e</u><u>e</u><u>d</u><u> </u><u>t</u><u>o</u><u> </u><u>a</u><u>s</u><u>k</u><u> </u><u>a</u><u>n</u><u>y</u><u> </u><u>question</u><u> </u><u>please</u><u> </u><u>l</u><u>e</u><u>t</u><u> </u><u>me</u><u> </u><u>know</u><u>.</u>

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If we were to foil
after experieence

we know
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and
in form
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if we expand it, we get
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compare to
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b=(bc+ad)
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in form
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or you could just expand it
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Simplify the expression <br><br> sin(pi+x) + sin(pi - x)
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3 years ago
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