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
cestrela7 [59]
3 years ago
7

the company also discovered that it costs 30 to 2 widgets, 118 to produce 4 and 766 to produce 10 widgets. Find the total cost o

f producing 6 widgets.
Mathematics
1 answer:
miv72 [106K]3 years ago
4 0

We will first write cost function. As we are given three points here so we will use them to write quadratic function

y = ax^{2} +bx+c----------------------------------------(1)

So we will plug point (2,30) in it first ( for 2 widgets cost is 30)

So simply plug 30 in y place and 2 in x place in equation (1) as shown

30 = a(2)^{2} +b(2)+c

30 = 4a +2b +c ----------------------------------------------(2)

Similarly plug next point (4,118) now in equation (1)

118 = a(4)^{2} +b(4)+c

118 = 16a +4b +c ----------------------------------------------(3)

Similarly plug third point (10,766) now in equation (1)

766 = a(10)^{2} +b(10)+c

766 = 100a +10b +c ----------------------------------------------(4)

Now we have to solve system of linear equations (2),(3) and (4) for a,b,c

We can use method of elimination

Subtract equation (3) - equation (2)

118 = 16a +4b +c

-(30 = 4a +2b +c)

----------------------------------------------------

88 = 12a +2b -----------------------------------(5)

Similarly subtract equation (4)-equation (3)

766 =100a +10b +c

-( 118 = 16a +4b +c)

--------------------------------------

648 = 84a + 6b ------------------------(6)

Now to eliminate b in equations (5) and (6) multiply equation (5) by -3 and then add to equation (6)

-3×(88 = 12a +2b)

-264 = -36a - 6b

648 = 84a + 6b

---------------------------------

384 = 48a

Now solve for a

\frac{384}{48} = \frac{48a}{48}

8 = a

Plug 8 in a place in equation (5) or (6) and solve for b as shown

88 = 12(8) +2b

88 = 96 + 2b

88 -96 = 96 +2b -96

-8 = 2b

\frac{-8}{2} = \frac{2b}{2}

-4 = b

now plug 8 in a place, -4 in b place in either of equations (2),(3) or (4) and solve for c

30 = 4(8) +2(-4) +c

30 = 32 -8 + c

30 = 24 + c

30 - 24 = 24 + c - 24

6 = c

So plugging values of a as 8, b as -4 and c as 6 in equation (1) we get

y = 8x^{2} -4x+ 6

So thats the cost function. So now for 6 widgets, plug 6 in x place in this equation and find y value

y = 8(6)^{2} -4(6)+ 6

y = 8(36) - 24 +6

y = 288 -24 +6

y = 270

So $270 is the cost for producing 6 widgets and thats the final answer

You might be interested in
B + 5/14 <br><br> b = 5/7<br> please help
Tatiana [17]
5/7 + 5/14 = 1.07142857143

you can round that to 1.1
4 0
3 years ago
Read 2 more answers
Be confident and be paitent to help people tahnky ou
Aleksandr [31]
12!!!! Hope this helped and good encouragement
4 0
3 years ago
Can someone please help me
MaRussiya [10]

Answer:

The answer is B)

Step-by-step explanation:

Use the Distance Formula

d = sqr(1 + 3)^2 + (0 - 4)^2

d = sqrt(32)

d = 4*sqrt(2)


7 0
3 years ago
On a certain hot summer day, 673 people used the public swimming pool. The daily prices are 1.75 for children and 2.00 for adult
amid [387]

Answer:

Number of children = 386

Number of adults = 287

Step-by-step explanation:

Let

x = number of children

y = number of adults

x + y = 673 (1)

1.75x + 2y = 1249.50 (2)

From (1)

x = 673 - y

Substitute x = 673 - y into (2)

1.75x + 2y = 1249.50

1.75(673 - y) + 2y = 1249.50

1177.75 - 1.75y + 2y = 1249.50

- 1.75y + 2y = 1249.50 - 1177.75

0.25y = 71.75

y = 71.75/0.25

y = 287

Substitute y = 287 into (1)

x + y = 673

x + 287 = 673

x = 673 - 287

x = 386

Number of children = 386

Number of adults = 287

3 0
3 years ago
PLS ANSWER TODAY TYSM :p<br><br> -5y+1-3y+2=-9
OLga [1]

We just combine the terms, like this:


-8y = -12


The answer is: y = 1.5 or 3/2.


Hope this helped! c:

7 0
3 years ago
Other questions:
  • How do you do this? Thanks for your time and effort!
    15·2 answers
  • How many 2/3 are in 8/9​
    9·2 answers
  • Hey there please help me with this question
    9·2 answers
  • 6010x98 equals ???????
    10·2 answers
  • I need help!!!!! due now!!!! plz!!!
    14·1 answer
  • What is the answer for -3(4x-2)&lt;18
    9·2 answers
  • Given that R = 6x + 9y
    14·1 answer
  • Find the two partial products in this problem. <br> 1,407x14
    8·1 answer
  • Austin correctly answered 80% of the questions on the geography quiz. Liz answered 42 of the 50 questions correctly. compare the
    7·1 answer
  • Sam opened a money-market account that pays 2% simple interest. He started the account with $7,000 and made no further
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!