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Oksi-84 [34.3K]
3 years ago
14

Divide. Express the quotient in simplest form.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0
( \frac{x^2 - x -12}{2x} ) ÷ ( \frac{x^2 - 2x - 8}{4x^2} )

= ( \frac{x^2 - x -12}{2x} ) × ( \frac{4x^2}{x^2 - 2x - 8} )

= \frac{x(x^2 - x -12)}{x^2 - 2x - 8}

= \frac{x(x^2 -4x +3x -12)}{x^2 -4x +2x -8}

= \frac{x[x(x - 4) +3(x - 4)]}{x(x - 4) +2(x - 4)}

= \frac{x(x-4)(x+3)}{(x-4)(x+2)}

= \frac{x(x+3)}{(x+2)}
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The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars
stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = 253x-2x^2

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

                      = 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= 253x-2x^2 - (3x + 6972)

= 253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

-2x^2+250x-6972=0\\

now we have to solve the above equation for x

Dividing both sides by -2 we get

x^2-125x+3486=0

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

5 0
3 years ago
CAN SOMEONE PLEASE HELP ME ASAP
Sunny_sXe [5.5K]

Answer:

G

Step-by-step explanation:

difference between coordinates of A and C is 9 because 7-(-2) is 9, one-third of nine is 3, -2+3=1 G is 1. (sorry for poor phrasing)

8 0
3 years ago
To make a homemade all purpose cleaner, you can use the ingredients shown in the table (1 cup vinegar, ½ cup of rubbing alcohol,
vovikov84 [41]

The total solution will include 17.5 cup of vinegar 0.5 cups of rubbing alcohol, and 2 cup of water which is a total of 35 cups of solution. Sofie will need 6 total containers to hold all of the solution.

<h3>Number of container</h3>

1 cup of rubbing alcohol:

1 cup of rubbing alcohol=1÷1/2

1 cup of rubbing alcohol=2

Cup of alcohol needed:

Cup of alcohol needed=1+1/2+16

Cup of alcohol needed=17.5 cups

Total cups:

Total cups=17.5×2

Total cups=35 cups

Number of container:

Number of container=1+35/5

Number of container=1+5

Number of container=6  containers

Therefore the total solution will include 17.5 cup of vinegar 0.5 cups of rubbing alcohol, and 2 cup of water which is a total of 35 cups of solution. Sofie will need 6 total containers to hold all of the solution.

Learn more about Number of container here:brainly.com/question/20533888

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5 0
1 year ago
What is the sum of 21 and 5 times a number f is 61
jasenka [17]

Answer:

f = 8

Step-by-step explanation:

21 + 5f = 61

5f = 61 - 21

f = (61 - 21) / 5

f = 8

5 0
3 years ago
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sorry don't know....

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