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solong [7]
3 years ago
8

A triangle has sides with lengths of 5x – 7,

Mathematics
1 answer:
Tom [10]3 years ago
4 0

Answer:

10x - 17

Step-by-step explanation:

Perimeter is the sum of all sides

5x - 7 + (3x - 4) + (2x - 6)

10x - 7 - 4 - 6

10x - 17

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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
HACTEHA [7]

Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

8 0
3 years ago
5.Sophia got 68 points correct on her math test, which earned her an 85%. Her friend Tami
Blababa [14]

Answer:

A 80 points, B 89%

Step-by-step explanation:

Look At The Attachment::

4 0
2 years ago
Read 2 more answers
How to factorize 2^{n+1}+2^{n-1}?<br><br>I know the answer is 5(2^{n-1}), but how do i get there?
Elina [12.6K]

Answer:

steps below

Step-by-step explanation:

2ⁿ⁺¹ +2ⁿ⁻¹ = 2ⁿ⁻¹ (2² + 1) = 5*2ⁿ⁻¹

7 0
3 years ago
A shipping container is in the shape of a right rectangular prism with a length of 13
Lilit [14]

Answer:

371 pounds

Step-by-step explanation:

First you find how much space is in the container

length is 13

width is 15

height is 10

2 * (15 * 13 + 10 * 13 + 10 * 15)= 950

The total space in the container is 950

Then multiply it by 0.39 to find the weight

950 * 0.39 = 370.5

Round to the nearest pound

.5 rounded is rounded to a whole number

371 pounds

8 0
3 years ago
IDK how to do this who else does
Nezavi [6.7K]

Answer:

36 ft²

Step-by-step explanation:

Scale factor means the side length are multiplied by some value.  Here, Jack takes 4 feet and multiplies it by a value of 1 1/2.  

The side length he wants is one and a half times the length of his neighbor's.  

The 'one' means the side length you started with, and the 'one half' means add half to the original length.

one and a half of four is six.  (4 plus half of 4, which is 2, so 4 plus 2)

The box is square, so each side is 6 ft, so the area of the box is 6x6 = 36 ft²

3 0
3 years ago
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