Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below: 3x + 12 + 2 = 2 + 5x – 20 3x + 14 = 5x – 18 14 = 2x

Answer:

a. i) Please refer to the attached graph representing the equation $10·x + $12·y = $300

ii) The intercepts indicate the maximum number of short-sleeve (at the x-intercept) and long-sleeve shirts (at the y-intercept) that can be ordered.

Step-by-step explanation:

The details provided are as follows:

Cost of each short-sleeve shirt = $10

Cost of each long-sleeve shirt = $12

Total budget available = $300

The equation for total spending is given by $10·x + $12·y = $300

Where;

x = Number of short-sleeved shirts

y = Number of long-sleeved shirts

Rearranging the equation into slope-intercept form, we have:

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Attached is the graph produced using Microsoft Excel

The coordinates that can be used for graph plotting are as follows:

x, y

(0, 25)

(5, 20.83)

(15, 12.5)

(20, 8.33)

(25, 4.17)

(30, 0)

The x-intercept denotes the quantity of short-sleeve shirts purchasable with a $300 budget, while the y-intercept signifies the quantity of long-sleeve shirts achievable under the same budget.

Answer:

Función de beneficios: P(x) = -0.5x^2 + 40x - 300

beneficio de $50: x = 10 y x = 70

NO es posible generar un ingreso de $2,500, ya que el máximo beneficio es de $500

Step-by-step explanation:

(Suponiendo que la función de ingresos es 90x−0.5x^2)

La función de costo está dada por:

Y la función de ingresos se expresa como:

La función de beneficios se determina restando los costos de los ingresos, por lo que tenemos:

Para encontrar los puntos donde los beneficios son $50, usamos P(x) = 50 y luego hallamos los valores de x:

Aplicando la fórmula de Bhaskara, obtenemos:

Los valores de x que resultan en un beneficio de $50 son x = 10 y x = 70

Para verificar si es posible obtener un beneficio de $2,500, necesitamos considerar el beneficio máximo, que es el máximo de la función P(x).

El valor máximo de P(x) se encuentra en el vértice. La coordenada x del vértice se calcula como:

Con este valor de x, podemos calcular el beneficio máximo:

El beneficio máximo es de $500, así que NO es posible generar un beneficio de $2,500.

Answer:

Raju's working time exceeded by 0.08 hours.

Answer:

Base Charge = $7

Additional Fees = $7

Step-by-step explanation:

Let x represent the base charge and y for the additional fees.

For a job that lasts 5 hours, we obtain:

For the 3-hour task

Finding x and y;

Deduct the second equation from the first

Calculate y

Replace 7 with y in the first equation