1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
strojnjashka [21]
3 years ago
7

The profit function for a product is given by p(x)=-x^3+3x^2+900x-2100, where x is the number of units produced and sold and P i

s in hundreds of dollars. Use factoring by grouping to find the numbers that will give a profit of $60,000.

Mathematics
1 answer:
nalin [4]3 years ago
3 0

Answer:

x = 30 and x = 3 both solve the equation correctly. See work below.

Step-by-step explanation:

The very first step is to realize that p(x) is in hundreds of dollars and that the given number is not. 60000 is not in hundreds of dollars. It is in dollars. 60000 dollars = 60000/100 = 600 hundreds of dollars.

Make the polynomial = 600

-x^3+3x^2+900x-2100 = 600  Subtract 600 from both sides

-x^3+3x^2+900x-2100 - 600 = 0  Combine

-x^3+3x^2+900x- 2700 = 0           Group  the first and second term and the Thrid and fourth terms.

(-x^2 + 3x^2) + (900x - 2700) = 0  Bring out the common factors from both groups.

-x^2(x - 3) + 900(x - 3) = 0 Factor out x - 3 on both sides of the plus sign

(- x^2 + 900)(x - 3) = 0       Reverse -x^2 + 900 to  900 - x^2

(900 - x^2)(x - 3) = 0          factor (900 - x^2) using the difference of squares

(30 - x)(30 + x) (x - 3) = 0

The two answers that work are

30 - x = 0                           Solve

- x = - 30                            Divide by - 1

-x/-1 = -30/-1                       Combine                          

x  = 30

============

x - 3 = 0

x = 3

===========

There are two values that will work to give p(x) = 600. There is no way to account for why both values work.

The graph below confirms both answers.


You might be interested in
DAVID PLZ HELP LAST ONE
Leto [7]

Answer:

1.D

2.c

Step-by-step explanation:

f(m/4)=8(m²/16)-4(m/4)

=m²/2-m

f(-4)=-3(-4)²+5(-4)

=-3(16)-20

=-48-20

=-68

3 0
3 years ago
Read 2 more answers
A customer purchased a total of 16 washcloths and towels. Each washcloth cost $10.50 and each towel cost $15.00. The customer sp
IgorC [24]

Answer:

3

Step-by-step explanation:

10.50 x 3 = 31.5

15 x 13 = 195

195 + 31.5 = 226.50

8 0
2 years ago
Estimate the sum of 487 and 310
Ronch [10]
487 + 310 ≈ 500 + 300 ≈ 800
3 0
3 years ago
Read 2 more answers
Please double-check for me :)
frosja888 [35]

<em>I think your answer is fine</em>

8 0
3 years ago
Question #2: Pythagorean Theorem
astra-53 [7]

Answer:

isnfdytsafksjd

Step-by-step explanation:

ryref w4trfd ws 3wqrs

3 0
3 years ago
Other questions:
  • Greg used 1 inch tiles to help make a ruler what mistake did he make
    11·1 answer
  • Explain how you could check the answer to a division question in which there is a remainder.
    15·1 answer
  • Solve by completing the square? Could you please work it out step-by-step?
    14·1 answer
  • NEED HELP ASAP
    9·1 answer
  • Henrique drew and labeled the net shown. He also labeled the areas of the left and right triangular sides.
    13·2 answers
  • use the points a(2, 3) and b(2, −5). complete the description of segment ab and find its length. then describe the image of segm
    8·1 answer
  • 10x-(8 + 7x)<br> SIMPLIFY IT ASAP PLEASE
    9·2 answers
  • Help I need this to help me get a grade 9
    6·1 answer
  • Need help with all , 50 points.
    10·1 answer
  • 2. The radius of a circle is 9 yards. Find the diameter.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!