A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit? StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 x squared + 11,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = 0.052 (x minus 500) squared + 24,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 11,000 EndLayout

StartLayout Enlarged Left-Brace 1st Row y = 280 x 2nd Row y = negative 0.052 (x minus 500) squared + 24,000 EndLayout

Step-by-step explanation:

Given that:

Cost per cleaner = $280

The cost of x vacuum cleaners will be :

Cost per cleaner * number of cleaners

$280 * x

= $280x

The general vertex firm equation :

y-k = a(x-h)^2

Vertex = (500, 24000) ; Vertex = (h, k)

h = 500 ; k =24000 y= 11000, x = 0

y intercept = 11000

Plugging the values :

11000 - 24000 = a(0 - 500)^2

- 13000 = a(-500)^2

-13000 = a * 250000

a = - 13000 / 250000

a = - 0.052

Hence,

y - 24000 = a(0 - 500)^2

y = - 0.052(0 - 500)^2 + 24000

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

then say something, tell them they won’t respect you if you don’t even have respect for your self sweetheart you need to lay it on them, all of it : )