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
icang [17]
2 years ago
5

A company’s profit in dollars is modeled by the equation p(x) = –0.5x2 + 100x, where x represents the number of units sold.

Mathematics
1 answer:
serg [7]2 years ago
6 0

Answers:

a. The company needs to sell 100 units to reach the maxmum profit.

b. The company's maximum profit is $5,000.

Solution:

a. How many unit does the company need to sell to reach the maximum profit?

p(x)=-0.5x^2+100x

This is a quadratic equation, and its graph is a parabola vertical (because the veriable "x" is square). Comparing with the general form:

p(x)=ax^2+bx+c; a=-0.5, b=100, c=0

a=-0.5<0 (negative), then the parabola opens downward, and it has a maximimun value (maximum profit) at its vertex.

We can find the abscissa of the vertex (units that the company needs to sell to reach the maximum profit using the following formula:

x=-b/(2a)

Replacing b by 100 and a by -0.5 in the formula above:

x=-100/[2(-0.5)]

x=-100/(-1)

x=100

The company needs to sell 100 units to reach the maximum profit.


b. What's the company's maximum profit?  

To determine the maximum profit we substitute the value of "x" obrained in part "a" in the quadratic equation:

x=100→p(100)=-0.5(100)^2+100(100)

p(100)=-0.5(10,000)+10,000

p(100)=-5,000+10,000

p(100)=5,000

The company's maximum profit is $5,000.

You might be interested in
A Walgreens purchase comes to $28. Find the total cost if a 2% sales tax is included.
OverLord2011 [107]

Answer:

The answer is $28.56

Step-by-step explanation:

To find the 2% sales tax, you need to multiply the 2% or 0.02 by 28.

Doing this will give you 0.56.

Then you add 0.56 to 28 to get 28.56, hence, $28.56 is the total cost.

Hope it helps!

4 0
3 years ago
Which of the following is a monomial?
KatRina [158]
The definition of monomial is an algebraic expression consisting of one term. 

a. 2xyz² is monomial.

b. 2x - yz is considered a binomial. (2 terms)

c. 2x + yz is considered a binomial. (2 terms)

d. 2 + xyz is also considered a binomial. (2 terms)

so the right answer is A.

hope this helped, God bless!
4 0
3 years ago
Find the equation for 4x/5=1/3(2x-15)
tia_tia [17]
4x / 5 = 1 / 3 ( 2x - 15 )
4x / 5= ( 2x - 15 ) / 3
4x × 3 = 5 ( 2x - 15 )
12x = 10x - 75
12x - 10x = - 75
2x = - 75
x = - 75 / 2
x = - 37.5
7 0
3 years ago
Which set of angle measures can be used to form a triangle ? A : 40 , 60 , 85 ,, B : 45 , 60 , 60 , C : 30 , 60 , 90 , D : 45 ,
Rainbow [258]

Answer:

D)45,90 90 this is the answer

3 0
3 years ago
Read 2 more answers
A church building fund has invested some money in two ways: part of the money at 7% interest and four times as much at 11%. Find
aliya0001 [1]

Answer: he invested $15000 in part 1 and $60000 in part 2

Step-by-step explanation:

Let x represent the amount of money invested in part one.

Let 4x represent the amount of money invested in part 2 .

Total amount of money invested in part 1 and part 2 is

x + 4x = 5x

The formula for simple interest is expressed as

I = PRT/100

Where

P is the principal or initial amount.

T is the duration in years

R is the number rate.

For part 1

R = 7%

T = 1 year

P = x

I = (x × 7 × 1)/100 = 0.07x

For part 2,

R = 11%

T = 1 year

P = 4x

I = (4x × 11 × 1)/100 = 0.44x

if the total annual income from interest is 7650. This means that

0.44x + 0.07x = 7650 - - - - - - - -2

0.51x = 7650

x = 7650/0.51

x = 15000

Amount invested in part 1 is $15000

Amount invested in part 2 is 4×15000 = $60000

4 0
3 years ago
Other questions:
  • If a stem and leaf has no number on one side what do you do
    11·1 answer
  • Ik this is easy but can someone help me?
    15·1 answer
  • What is the solution of the system? Use substitution. y = x + 6 y = 2x
    8·1 answer
  • What fraction can you find between 2/3 and 1/4?
    10·2 answers
  • Write an exponential function in the form y = ab that goes through points (0,4)<br> and (2, 196).
    12·1 answer
  • The equation below describes a parabola. If ais negative, which way does the<br> parabola open?
    15·2 answers
  • What is the Hypotenuse of 12mi and 16mi
    13·1 answer
  • I NEED HELP ✋!!!!!!!!!!!!!!!!!!!L!!!!!!!!!!!!
    12·1 answer
  • Write the decimal 4.005 as a fraction in the simplest form​
    7·2 answers
  • If (x2 – 4) ÷ (x 2) = x – 2, which polynomial should fill in the blank below? (x 2) ´ ______ = x2 – 4
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!