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3 years ago

1. Complete this statment: A polygon with all sides the same length is said to be____

Mathematics

1 answer:

Katen [24]3 years ago

8 0

Answer:

Q1. Regular (A)

Q2. 105° (C)

Q3. x=45°

Step-by-step explanation:

Q1. A regular polygon is a polygon with all sides and angles equal.

Q2. The sum of the measure of exterior angles of a polygon is always 360°. Therefore, 360°-255°=105°

Q3. 148°+112°+(2x+10)°+(2x)°+90°= Sum of angles in a pentagon.

Note: The square at the fifth angle shows that its a right angle which is 90°. Also all the angles are equal to the sum of angles in a pentagon 'cause the polygon has 5 sides ( a pentagon).

Sum of interior angles of a polygon is: (n-2)180°. Where "n" is the number of sides of the polygon.

Therefore the sum of interior angles is (5-2)180°=540°

solving the equation you have;

360°+4x=540°

4x=540°-360°

4x=180°

x=180°/4

x=45°

therefore x=45°

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3 years ago

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals72 com

solmaris [256]

Answer:

Part (A)

1. Maximum revenue: $450,000

Part (B)

2. Maximum protit: $192,500

3. Production level: 2,300 television sets

4. Price: $185 per television set

Part (C)

5. Number of sets: 2,260 television sets.

6. Maximum profit: $183,800

7. Price: $187 per television set.

Explanation:

0. Write the monthly cost and price-demand equations correctly:

Cost:

$C(x)=72,000+70x$

Price-demand:

$p(x)=300-\dfrac{x}{20}$

Domain:

$0\leq x\leq 6000$

1. Part (A) Find the maximum revenue

Revenue = price × quantity

Revenue = R(x)

$R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x$

Simplify

$R(x)=300x-\dfrac{x^2}{20}$

A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.

$R'(x)=300-\dfrac{x}{10}$

Solve for R'(x)=0

$300-\dfrac{x}{10}=0$

$3000-x=0\\\\x=3000$

Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.

Hence, the maximum revenue is obtained when the production level is 3,000 units.

And it is calculated by subsituting x = 3,000 in the equation for R(x):

R(3,000) = 300(3,000) - (3000)² / 20 = $450,000

Hence, the maximum revenue is $450,000

2. Part (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. 

i) Profit(x) = Revenue(x) - Cost(x)

Profit (x) = R(x) - C(x)

$Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)$

$Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000$

ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)

Profit' (x) = -x/10 + 230

-x/10 + 230 = 0

-x + 2,300 = 0

x = 2,300

Thus, the production level that will realize the maximum profit is 2,300 units.

iii) Find the maximum profit.

You must substitute x = 2,300 into the equation for the profit:

Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500

Hence, the maximum profit is $192,500

iv) Find the price the company should charge for each television set:

Use the price-demand equation:

p(x) = 300 - x/20

p(2,300) = 300 - 2,300 / 20

p(2,300) = 185

Therefore, the company should charge a price os $185 for every television set.

3. Part (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?

i) Now you must subtract the $4 tax for each television set, this is 4x from the profit equation.

The new profit equation will be:

Profit(x) = -x² / 20 + 230x - 4x - 72,000

Profit(x) = -x² / 20 + 226x - 72,000

ii) Find the first derivative and make it equal to 0:

Profit'(x) = -x/10 + 226 = 0

-x/10 + 226 = 0

-x + 2,260 = 0

x = 2,260

Then, the new maximum profit is reached when the production level is 2,260 units.

iii) Find the maximum profit by substituting x = 2,260 into the profit equation:

Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000

Profit (2,260) = 183,800

Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800

iv) Find the price the company should charge for each set.

Substitute the number of units, 2,260, into the equation for the price:

p(2,260) = 300 - 2,260/20

p(2,260) = 187.

That is, the company should charge $187 per television set.

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3 years ago

Jenny wants to serve fruit punch at her party. She plans to buy a punch bowl that costs 5$ and fruit punch that costs 1.40$ per

krek1111 [17]

The answer is Y=1.40p+5

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3 years ago

Find the slope if it exits 2x-5y=6

77julia77 [94]

In standard form, slope is always the negative of the x coefficient over the y coefficient.

If you dont want to have that memorized, you can use algebra to get the equation of the line into slope-intercept form (y=mx+b)

Set it equal to y

2x - 5y = 6
2x = 5y + 6
2x - 6 = 5y
(2/5)x - 6/5 = y
Now it is in slope intercept form. In slope intercept form, the coefficient multiplying with x is the slope of the line. Therefore, the slope equals 2/5.

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Charra [1.4K]

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