En una piscina hay 1500 litros y el desagüe bota en el despiche medio litro por minuto. La función que describe la cantidad de litros (lt) que habrá en la piscina a las x horas después de abrir el despiche del desagüe es

1500 - 30x

Step-by-step explanation:

Aquí, queremos obtener una función que describa la cantidad de litros que quedan en la piscina a las x horas después de abrir la salida de drenaje.

De la pregunta, la capacidad total de la piscina. es de 1.500 litros.

La tasa de goteo es de 0,5 litros por minuto.

x horas es lo mismo que 60 * x = 60x minutos

La cantidad de litros caídos en 60x minutos será 60x * 0,5 litros = 30x litros.

Entonces el número de litros que quedan será; 1500 - 30x

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

the third picture

step-by-step explanation: