Question

Please help? algebra 1

Answer 1

1)
`\text{Revenue}=0.25x^2+500x`

2) The flat-fee delivery is $500.

Step-by-step explanation:

Given : A tile factory earns by charging a flat fee for delivery and a sales price of $0.25 per tile.One customer paid a total of $3,000 for 10,000 tiles.The equation
`y-3,000=0.25(x-10,000)` models the revenue of the tile factory,where x is the number of tiles and y is the total cost to the customer.

To find :

1) Which function describes the revenue of the tile factory in terms of the tiles sold?

Total cost is

`y-3,000=0.25(x-10,000)`

`y=0.25x-10000* 0.25+3000`

`y=0.25x-2500+3000`

`y=0.25x+500`

Revenue is defined as
`\text{Revenue}=\text{Quantity}* \text{Cost}`

`\text{Revenue}=x* (0.25x+500)`

`\text{Revenue}=0.25x^2+500x`

2) What is the flat-fee for delivery?

The flat-fee delivery is given by the y-intercept of the linear function, i.e. the value of y when x = 0

So, substitute x=0 in
`y=0.25x+500`

`y=0.25(0)+500`

`y=500`

Therefore, the flat-fee delivery is $500.

Answer 2

Question 1. What function describes the revenue of the tile factory in terms of the tiles sold?

• y = 0.25x + 5,500

Question 2. What is the flat-fee for delivery?

• $5,500

Step-by-step explanation:

The equation y - 3,000 = 0.25(x - 10,000) is a linear function written in point-slope form.

• 0.25 represents the slope of the line and is the unit sales price ($ 0.25 per tile).

• (10000, 3000) is the point that represents the sale of 10,000 tiles with a total revenue of $3,000

To answer the first question, you can clear the dependent variable, y, in terms of the independent variable, x:

• y = (0.25x - 10,000) + 3,000

• y = 0.25x + 2,500 + 3,000

• y = 0.25x + 5,500

And that is the function that describes the revenue of the tile factory in terms of thenumber of tiles sold.

To answer the second question, the flat-fee delivery, you find the y-intercept of the linear function, i.e. the value of y when x = 0:

• y = 0.25(0) + 5,500

• y = 5,500

Hence the flat-fee delivery is $ 5,500.