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harkovskaia [24]
3 years ago
8

A small business produces and sells balls. The fixed costs are $20 and each ball costs $4.32 to produce. Each ball sells for $8.

32. Write the equations for the total cost, C, and the revenue, R, then use the graphing method to determine how many balls must be sold to break even.

Mathematics
1 answer:
Gemiola [76]3 years ago
5 0

Part 1:

Fixed Cost, f = $20

number of balls = n

Cost of each ball, c = 4.32

Price of each ball, p = 8.32

Equation for total cost:

Total Cost of balls will come by adding the cost of all balls and the fixed cost

Total Cost = number of balls made × Cost of each ball + fixed cost

<em>C = 4.32n + 20</em>

Equation for revenue:

Revenue  = Number of balls made × price of each ball

<em>R =  8.32n </em>

Part 2:

Use the graphing method to determine how many balls must be sold to break even

Breakeven means Revenue =  total Cost

This happens at a point (5,41.6) where n = 5 is the number of balls sold

and C = 41.6 is the total cost

When 5 balls are sold there will be breakeven

R = 4n - 20  

C = 4.32n + 20

Red line represent Cost

Black line represent Revenue

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docker41 [41]

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

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3 years ago
A parallelogram is shown below:
Marina CMI [18]
<h3>Answer:</h3>

A:  6 ft²

B:  3 ft² is the area of each of the two congruent triangles

<h3>Step-by-step explanation:</h3>

Part A. As with a rectangle, the area of a parallelogram is the product of base length and height.

  Area = (8 ft)·(3/4 ft) = 6 ft²

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Part B. If you cut the area into two halves, each half will have half the area of the original. (That should not be a surprise.)

  triangle area = (6 ft²)/2 = 3 ft²

If the triangles are created by a diagonal across the original figure, each will have a base length and height that is the same as that of the original figure. The area of a triangle is half the product of base and height, so each triangle will have area ...

  triangle area = (1/2)bh = (1/2)(8 ft)(3/4 ft) = 3 ft²

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Answer:

SSS and SAS

Step-by-step explanation:

Law of cosines: The law of cosines is used for calculating one side of a triangle when the angle opposite and the other two sides are known.

If the information about a triangle according to SSS, SAS and ASA is given, then we will immediately use SSS and SAS  by using the law of cosines to find one of the remaining measures because Law of cosines is applied if we know one angle opposite and the other two sides.

Also, in ASA, we know two angles and one side, thus we cannot use Law of cosines in this, rather Law of sines can be accurately use in this case.

if you have two sides, encroaching an angle, then the Law of Cosines can be used to find a missing side, thus SAS will work fine for that, now, if you have no angles given, but you know all sides, you can use the Law of Cosines as well, by solving it for the angle, and get the angles, on which case, SSS will do... .now as far as ASA, if you have two angles and one side known, then... that's not very workable for the law of cosines

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3 years ago
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Type the correct answer in each box use numerals instead of words if nessasary us /for fractions subtract write your amswer in s
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converting mixed fractions to improper fractions.

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As there are no common terms to cancel it is in lowest form.

Hence, the lowest form of the given expression is \frac{31}{12}

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An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
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The 3rd option or 39,600 would be the correct answer.

Step-by-step explanation:

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