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
Harrizon [31]
3 years ago
7

Company ABC produces widgets. They have found that the cost, c (x), of making x widgets is a quadratic function in terms of x. T

he company also discovered that it costs $23 to produce 2 widgets, $55 to produce 4 widgets, and $247 to produce 10 widgets. What is the total cost of producing 8 widgets?
Mathematics
2 answers:
maw [93]3 years ago
6 0

We can solve this with the following system

 

a(2)^2  + b(2) + c = 23

a(4)^2 + b(4) + c = 55

a(10)^2 + b(10) + c  = 247      simplifying, we have

 

4a + 2b + c  = 23            (1)

16a + 4b + c = 55           (2)

100a + 10b + c   = 247     (3)

 

Subtract (1) from (2)    and  (2) from (3)    ...and we get the following system

 

12a + 2b  =   32

84a + 6b  =  192       these simplify to

 

6a + b = 16    →    b =  16 - 6a    (4)

28a + 2b  = 64        (5)

 

Substitute   (4) into (5)

 

28a + 2[16 - 6a] = 64   simplify

28a + 32 - 12a  = 64

16a + 32 = 64    subtract 32 from both sides

16a  = 32      divide both sides by 16

a = 2

 

And using (4)  .....

  b =  16 - 6(2)  = 16 - 12  = 4

 

 

And using (1) ......

4(2) + 2(4) + c = 23

8 + 8 + c = 23

16 + c = 23

So    c  = 7

 

And our cost function is :

 

c(x)  = 2x^2 + 4x + 7       and the cost to produce 8 widgets is

c(8)  = 2(8)^2 + 4(8) + 7   =   2*64 + 32 + 7  =  128 + 39  = $ 167

 

Tju [1.3M]3 years ago
5 0
Well the table function I got was 2 x^2+4 x+7
So I got 8 widgets = $167
You might be interested in
78 is what percent of 110
irinina [24]

Answer: 70.909090909091%

Step-by-step explanation: Reading through the problem we have <em>78 is</em>, that's 78 equals, <em>what percent</em>, x/100, <em>of 110</em>, times 110.

It's important to understand that <em>percent</em> means over 100 so what percent would simply mean <em>x/100</em> or any variable but I will be using x.

So we have the equation 78 = \frac{x}{100} *110

So cross canceling the 110 and 100 to 11 and 10, we have 78 = \frac{11x}{10}

Multiply both sides by 10 to get rid

of the fraction and we have 780 = 11x.

Now divide both sides by 11 and 70.909090909091 = x.

So, 78 is 70.909090909091% of 110.

Work is attached in the image provided.

8 0
3 years ago
What is the length of line segment EF?
luda_lava [24]
The answer to this problem is...3.6
8 0
3 years ago
Read 2 more answers
Please just answer with a picture
PIT_PIT [208]
From the instructions i gather it might be like this

8 0
3 years ago
Is 24 root 4 or 16 bigger
alexdok [17]

Answer:

no

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What does the graph of -3x-5y≥20 look like?
Hoochie [10]
The answer is D I believe
8 0
3 years ago
Other questions:
  • 1 1/2= v + 3/4 (that's 1 and a half, not 11 over 2)<br> what is v?
    5·2 answers
  • The population of a local species of mosquitos can be found using an infinite geometric series where a1 = 740 and the common rat
    15·1 answer
  • Please help??? thanks!!!
    12·1 answer
  • X2 + 12x =<br> – 20<br> what are the roots of the following quadratic equation
    15·1 answer
  • Forces of 420 kg and 300 kg act on an object. The angle between the forces is 50°. Find the resultant, giving the angle it makes
    7·1 answer
  • Help? Plz I need help
    10·1 answer
  • A number cube is rolled 24 times and the results are recorded as follows: 2 ones, 4 twos, 7 threes, 4 fours, 3 fives, and 4 sixe
    11·1 answer
  • What is 61.1% of 54? as decimal
    13·2 answers
  • - 3x + y = 3<br> 2y = -3x - 12
    8·1 answer
  • How do you write (4)(25)-300 as an addition equation
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!