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3 years ago

-3x -4y = 20 x - 10y =16 if (x, y) is the solution to the system of equations above what is the value of x?

1 answer:

6 0

Multiply first equation by -5 and 2nd by 2, add them

15x+20y=-100
<u>2x-20y=32 +</u>
17x+0y=-68

17x=-68
divide both sides by 17
x=-4

the x value is -4

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13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Vera_Pavlovna [14]

Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

$5+5^{2}=30$ (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

$5^{1}+5^{2}+5^{3}+...+5^{x}>19000$ (II)

Buscamos el valor de $x$ que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

$5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000$

$19530>19000$

El valor de $x$ que satisface (II) es $x=6$ .

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro $x=6$ , el número de horas que pasaron son 5 horas (1 menos que el valor de $x$ )

Todo el pueblo se habrá enterado en 5 horas de la noticia.

7 0

3 years ago

HHHHHHHHHHEEEEEEEEELLLLLLLLLLLPPPPPPPPPP

Nastasia [14]

Answer:

I'm pretty sure it is 18

Step-by-step explanation:

Since the shape is not a perfect square you can count how many blocks are shaded. However, the half shaded blocks, since they are half shaded you will need 2 half shaded blocks to make one block

5 0

3 years ago

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

2 years ago

Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to s

erik [133]

Answer:

.00059 or .0006

Step-by-step explanation:

You are trying to find what won't be in the water because there are many combinations so you use a complement formula.

1-0.79=0.29

Use the left over percentage in an equation to determine the probability.

$1-(0.29)^6=0.000594823$

The exponent 6 comes from the number of locations.

8 0

3 years ago

AHHH PLS HELP QUICK ILL GIVE U BRAINLIEST <3

nika2105 [10]

Answer:

Step-by-step explanation:

19 divided by 19 is equal to 1 so you cross out 19 and are left with "b".

190 divided by 19 is equal to 10.

b=10

7 0

3 years ago

Read 2 more answers