If the cost. C, for manufacturing x units of a certain product is given by C= x² + 10x +30, find the number of units manufactured at a cost of $11,030.

  100 units

Step-by-step explanation:

We want to find x when ...

  C = 11030

  x² +10x +30 = 11030 . . . . fill in for C

  x² +10x = 11000 . . . . . . . . subtract 30

  x² +10x +25 = 11025 . . . . add 25 to complete the square

  (x +5)² = 105² . . . . . write as squares

  x +5 = ±105 . . . . . . . take the square root

  x = -5 ±105 = {-110, 100}

The number of units manufactured at a cost of $11,030 is 100.

The number of units manufactured at a cost of $11,030 was 100.

Step-by-step explanation:

I graphed the function on the graph below and found the point where C = 11,030. When C = 11,030, x is 100

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: