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Mama L [17]
2 years ago
8

a ferry is traveling at a constant speed back to the dock, as shown in the graph. which function represents the relationship bet

ween the distance from the ferry to the dock in miles, y, and the time that the ferry has been traveling toward the dock in hours, x?
Mathematics
1 answer:
horsena [70]2 years ago
6 0

Answer: y = -35x + 105

Step-by-step explanation:

The graph represents a function that is between hours and miles and to determine the equation which belong to this graph, we need to find the slope first by using two points from the graph which are (0, 105) and (3, 0).

The definition of slope is

m = (y2 - y1)/(x2 - x1)

= (0-105)/3-0

= -105/3

= -35

The slope is -35 and remember that the slope is the coefficient of the variable x. Therefore, the answer is:

y = -35x + 105

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Step-by-Step explanation:

Translation (x+5, y-3) is the movement of LMNP five units to the right and three units down

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Greg is 3 years older than Kevin. In seven years, the sum of their ages will be 41. How old is each now ?
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Let their ages be g and k.  Then g = k + 3.

Next:  (g+7) + (k+7) = 41.

Substituting k + 3 for g in the above equation, we get  k + 3 + 7 + k + 7 = 41.

Combining like terms:  2k + 17 = 41.  Then 2k = 24, and k = 12.

Kevin is 12 years old and Greg is 15 years.

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1. De una encuesta realizada a 120 personas sobre el consumo de albaricoque, banana y coco se obtuvieron el siguiente resultado.
Pachacha [2.7K]

Answer:

El número de personas que consumen dos productos es 30.

Step-by-step explanation:

El primer paso para resolver el problema es realizar los gráficos de los eventos (agregaré como archivo adjunto el gráfico del ejercicio).

En el gráfico podemos ver 7 regiones :

A : Personas que consumen sólo albaricoque.

B : Personas que consumen sólo banana.

C : Personas que consumen sólo coco.

D : Personas que consumen sólo albaricoque y coco.

E : Personas que consumen las tres frutas (albaricoque, banana y coco).

F : Personas que consumen sólo banana y coco.

G : Personas que consumen sólo albaricoque y banana.

Ahora, debemos escribir las ecuaciones que nos brinda el ejercicio :

La encuesta se realizó a 120 personas y se sabe que todas las personas consumen un producto ⇒

A+B+C+D+E+F+G=120 (I)

''El número de personas que consumen sólo albaricoque y coco es la mitad de las que consumen sólo albaricoque''  ⇒

D=\frac{A}{2} (II)

''El número de personas que consumen sólo banana es el doble de las personas que consumen sólo albaricoque y banana más sólo banana y coco'' ⇒

B=2.(G+F) (III)

Finalmente : ''El número de personas que consumen sólo coco más los que consumen los tres productos es 30''  ⇒

C+E=30 (IV)

Finalmente obtenemos el siguiente sistema de ecuaciones :

A+B+C+D+E+F+G=120\\D=\frac{A}{2}\\B=2.(G+F)\\C+E=30

El número de personas que consumen dos productos es :

D+F+G

Entonces, resolvemos escribiendo la primera ecuación conmutando los términos :

A+B+C+E+D+F+G=120 (V)

De (II) se obtiene :

2D=A (VI)

Usamos (VI), (III) y (IV) en (V) ⇒

2D+2(G+F)+30+D+F+G=120  ⇒

2D+2G+2F+30+D+F+G=120

3D+3F+3G=90

Dividiendo esta última ecuación por ''3'' obtenemos :

D+F+G=30

Que es el número de personas que consumen dos productos.

Es muy conveniente seguir el desarrollo del ejercicio mirando el gráfico que adjunto.

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