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EastWind [94]
3 years ago
8

Un padre para estimular a su hijo para estudiar matemáticas le dice: por cada ejercicio que resuelvas bien te daré 7 € y por cad

a uno que hagas mal me darás 1 €. Después de hacer 45 ejercicios, el muchacho se encuentra con 19 €. ¿Cuántos ejercicios ha resuelto bien?
Mathematics
1 answer:
Naya [18.7K]3 years ago
8 0

Answer:

8 ejercicios

Step-by-step explanation:

De acuerdo a la información dada, puedes plantear las siguientes ecuaciones:

x+y= 45 (1)

7x-1y= 19 (2)

x= ejercicios que resolvió bien

y= ejercicios que resolvió mal

Primero, puedes despejar x en (1):

x= 45-y (3)

Segundo, debes reemplazar (3) en (2):

7(45-y)-1y=19

315-7y-1y= 19

315-8y= 19

315-19= 8y

296= 8y

y= 296/8

y= 37

Tercero, debes reemplazar el valor de y en (3) para encontrar x:

x= 45-37

x= 8

De acuerdo a esto, la respuesta es que el hijo ha resuelto bien 8 ejercicios.

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kherson [118]

Step-by-step explanation:

The equation of a circle can be the expanded form of

\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a)

2

+(y−b)

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where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.

Here, the equation of the circle is,

\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered}

⟹

⟹

⟹

⟹

x

2

+y

2

+10x−4y−20

x

2

+y

2

+10x−4y+25+4−49

x

2

+y

2

+10x−4y+25+4

x

2

+10x+25+y

2

−4y+4

(x+5)

2

+(y−2)

2

=

=

=

=

=

0

0

49

49

7

2

From this, we get two things:

\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered}

1.

2.

Center of the circle is (−5, 2).

Radius of the circle is 7 units.

Hence the radius is 7 units.

4 0
2 years ago
What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?
loris [4]

Answer:

<em>The coordinates of the vertex are (-1,-4).</em>

Step-by-step explanation:

<u>Equation of the Quadratic Function </u>

The vertex form of the quadratic function has the following equation:

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