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g100num [7]
3 years ago
15

Simplify. show your work on a plz

Mathematics
1 answer:
Reptile [31]3 years ago
6 0

[(3x^2y^3)^2]3

work from the inside out

(3x^2y^3)^2

3^2 (x^2)^2 (y^3)^2

x^2^2 multiply the exponents  =x^4

y^2^3 = y^6

9 x^4 y^6

[9x^4 y^6]^3

9^3 x^4^3 y^6^3

729 x^12 y^18

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An investor obtains a balloon mortgage with the terms shown below.
Flauer [41]

9514 1404 393

Answer:

  a.  $3,455.20

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

for loan amount P at annual rate r for t years.

For this mortgage, we use P = $530,000, r = 0.068, t = 30.

  A = $530,000(0.068/12)/(1 -(1 +0.068/12)^(-360)) ≈ $3,455.20

The monthly payment is $3,455.20.

_____

<em>Additional comment</em>

In 7 years, the balloon payment will be $481,559.91.

6 0
2 years ago
Write each product using an exponent.<br><br> 9 × 9 × 9 × 9
ki77a [65]

Answer:

9^4 is what you’re looking for right?

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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
2 years ago
Find the slope of the line passing through the points(-3, 7) and (2, -6).
postnew [5]

Answer:

-13/5

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

-6-7/2-(-3)

-13/5

Best of Luck!

4 0
2 years ago
Algebra problem, please show work!
Brrunno [24]

6x+1 / 2x +6 - 5/2

Factor 2 out of the denominator of the first fraction:

6x+1 / 2(x+3) - 5/2

Rewrite 5/2 to have a common denominator with the first fraction:

6x+1/2(x+3) - 5(x+3) / 2(x+3)

Simplify terms:

6x +1 - 5(x+3) / 2(x+3)

Use distributive property:

6x +1 - 5x -15 / 2(x+3)

Combine like terms for final answer:

(x-14) / 2(x+3)

4 0
3 years ago
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