Widget wonders produces widgets. they have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.....the company also discovered that it costs $103. to produce 3 widgets, $163 to produce 7 widgets, and $328 to produce 12 find the total cost of producing 2 widgets

Answers

Answer 1

Answer: $c(x)=ax^2+bx+c \n \nc(3)=103 \nc(7)=163 \n c(12)=328 \n \na * 3^2+b * 3 + c=103 \na * 7^2 + b * 7 + c= 163 \na * 12^2 + b * 12 + c =328 \n \n9a+3b+c=103 \n49a+7b+c=163 \n144a+12b+c=328$

$\hbox{the first two equations:} \n9a+3b+c=103 \ \ \ \ \ |* (-1) \n49a+7b+c=163 \n \n-9a-3b-c=-103 \n\underline{49a+7b+c=163 \ \ \ \ \ } \n40a+4b=60 \ \ \ \ \ \ \ \ \ \ \ |/ 4 \n10a+b=15$

$\hbox{the second and third equation:} \n49a+7b+c=163 \ \ \ \ \ \ \ |* (-1) \n 144a+12b+c=328 \n \n-49a-7b-c=-163 \n\underline{144a+12b+c=328 \ \ } \n95a+5b=165 \ \ \ \ \ \ \ \ \ \ \ \ |/ 5 \n19a+b=33$

$\hbox{set up a new system of equations:} \n10a+b=15 \ \ \ \ \ \ \ \ |* (-1) \n19a+b=33 \n \n-10a-b=-15 \n\underline{19a+b=33 \ \ \ \ \ \ } \n9a=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 9 \na=2 \n \n10a+b=15 \n10 * 2+b=15 \n20+b=15 \ \ \ \ \ \ \ \ \ \ |-20 \nb=-5$

$49a+7b+c=163 \n49 * 2+7 * (-5)+c=163 \n98-35+c=163 \n63+c=163 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |-63 \nc=100 \n \n\hbox{the equation for the cost of maxing x widgets:} \nc(x)=2x^2-5x+100 \n \nc(2)=2 * 2^2-5 * 2+100=8-10+100=98$

The cost of producing 2 widgets is $98.

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Plz help on numbers 18-20 with work and answer shown plz

Answers

Hope this helps! If there's any question then leave a comment.

Find a fraction in between 21/34 and 34/55

Answers

Answer:

2311/3740

Step-by-step explanation:

34 = 2×17

55 = 5×11

LCM = 2×5×11×17 = 1870

⁵⁵⁾21/34 = ²⁾1155/1870 = 2310/3740

³⁴⁾34/55 = ²⁾1156/1870 = 2312/3740

2310/3740 < 2311/3740 < 2312/3740

Answer:

A fraction between that is 2311/3740

Step-by-step explanation:

This is because the denominator is simplified into one number and the fraction is taken from there.

Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.y = x + 8
y = x − 8
y = −5x − 10
y = −5x + 20

Answers

m = (y2 -y1)/(x2-x1)
m = (10 -5 )/(2+3)
m = 5 / 5
m = 1

using y = mx + b passing through (−3, 5)
5 = 1(-3) + b
5 + 3 = b
so b = 8

equation

y = x + 8

answer: y = x + 8 (first choice)

first you have to find the slope by doing y2-y1 / x2-x2 which will be 10-5 over 2-(-3)

Simplify and you get 5/5 which is one

Now solve for d by plugging a set of points back in and you get 8=d

so y=x+8

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) Step 1: 12 + (–3)·(–2x) + (–3)·(4)
Step 2: 12 + 6x + (–12)
Step 3: 12 + (–12) + 6x
Step 4: 0 + 6x Step 5: 6x

What property of real numbers was used to transition from Step 3 to Step 4?
A. identity property of addition
B. inverse property of addition
C. associative property of addition
D. commutative property of addition