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2 years ago

A) 0.15 B) an equal sign C) a multiplication sign D) a percent sign

Mathematics

1 answer:

nekit [7.7K]2 years ago

8 0

Answer:

Step-by-step explanation:

What is 15% of 60 is nothing but What equals 15% of 60 or What = 15% of 60

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Identify the restrictions on the variable

34kurt

Answer:

x ≠ -4

Step-by-step explanation:

Division by zero is not defined, so x cannot = -4.

8 0

2 years ago

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per

dexar [7]

Answer:

The total revenue is $TR=580x-10x^2$ .

The marginal revenue is $MR=580-20x$ .

The fixed cost is $900.

The marginal cost function is $MC=50x+300$ .

Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

$TR=p\cdot x$

The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

$MR=\frac{d(TR)}{dx}$

From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

$TR=(580-10x)\cdot x\\TR=580x-10x^2$

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

The Fixed Cost ( $FC$ ) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

$MC=\frac{d(TC)}{dx}$

We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$

4 0

2 years ago

Point A has coordinates (3, 4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down

adelina 88 [10]

(-1, 2)

So the original point is (3, 4), when you move to the left or right, it changes the x value. When moving it to the right, you add the amount. When moving to the left, you subtract the amount

So after translating the point 4 units to the left, it should be (-1, 4).

Now, you have to move down. When moving up and down, you add or subtract to the y value. When moving up, you add to the amount. When moving down, you subtract the amount.

After subtracting 2, you should be at (-1, 2)

4 0

2 years ago

Question in picture above ^

Andrei [34K]

[ 4(4) x 4(3) ] / 4(5)

= [4(4+3)] / 4(5)

= 4(7) / 4(5)

= 4(7-5)

= 4(2)

5 0

2 years ago

Find the inverse of each of the given functions.

Leona [35]

Answer:

The inverse of the function is (3x+4)/2

Step-by-step explanation:

To find the inverse, exchange x and y and then solve for y

y = (2x-4) /3

Exchange x and y

x = (2y-4)/3

Solve for y

Multiply each side by 3

3x = (2y-4)/3 *3

3x =2y-4

Ad 4 to each side

3x+4 = 2y-4+4

(3x+4) =2y

Divide each side by 2

(3x+4)/2 =2y/2

(3x+4)/2 = y

The inverse of the function is (3x+4)/2

6 0

2 years ago

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