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3 years ago

Simplify. Assume that no denominator is equal to zero.

Mathematics

1 answer:

aivan3 [116]3 years ago

6 0

Answer: FIRST OPTION.

Step-by-step explanation:

For this exercise it is important to remember a property called "Quotient of Powers property".

By definition the Quotient of Powers property states the following:

$\frac{a^m}{a^n}=a^{(m-n)}$

You can observe the division of $a^m$ and $a^n$ . Since both have the same base "a" , you must rewrite the base and subtract the exponents "m" and "n".

In this case, you have the following expression given in the exercise:

$\frac{4^{12}}{4^{5}}$

Then, you need to apply the Quotient of Powers property rewriting the base 4 and subtracting the exponents 12 and 5.

Therefore, you get the following result:

$=4^{(12-5)}=4^7$

You can notice that it matches with the first option.

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A manufacturer has been selling 1000 flat-screen TVs a week at $500 each. A market survey indicates that for A manufacturer has

luda_lava [24]

Answer:

a) Demand function: $q=6000-10\cdot p$

b) The rebate should be of $200, so the sale price becomes $300 per unit.

c) The rebate should be of $150, so the sale price becomes $350 per unit.

Step-by-step explanation:

a) In this case, we have a known point of the demand function (1000 units sold at $500), and the slope of a linear function (increase by 100 units fora decrease in $10).

We can express the demand function (linear) as:

$q=b+m\cdot p$

To calculate the slope m, we use:

$m=\Delta q/\Delta p=(+100)/(-10)=-10$

To calculate b, we use the known point and the calculated slope:

$q=b+m\cdot p\\\\b=q-m\cdot p=1000-(-10)\cdot (500)=1000+5000=6000$

Then the demand function is:

$q=6000-10\cdot p$

b) The revenue can be expressed as:

$R=q\cdot p = (6000-10p)\cdot p=6000p-10p^2$

To maximize, we can derive and equal to zero

$dR/dp=6000-2*10p=0\\\\20p=6000\\\\p=300$

The rebate should be of $200, so the sale price becomes $300 per unit.

c) If we take into account the cost, we have that

$R=q\cdot p-C=(6000p-10p^2)-(68000+100q)\\\\R=(6000p-10p^2)-(68000+100(6000-10p))\\\\R=6000p-10p^2-(68000+600000-1000p)\\\\R=-10p^2+7000p-668000$

To maximize, we can derive and equal to zero

$dR/dp=-20p+7000=0\\\\p=7000/20=350$

The rebate should be of $150, so the sale price becomes $350 per unit.

5 0

3 years ago

Rewrite the expression with the given base. 25^3x with a base of 5.

svp [43]

$Use\ (a^n)^m=a^{nm}\\\\25^{3x}=(5^2)^{3x}=5^{2\cdot3x}=5^{6x}$

6 0

3 years ago

Which two equations would be represented as parallel lines?

Mariana [72]

Answer:

The first and third options are parallel.

Step-by-step explanation:

They both have a slope of 2.

Pls mark brainliest. Thanks!

4 0

3 years ago

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Explain how you would find the sum of 46+7

Darya [45]

Answer: Method of finding the sum of 46 and 7 is mentioned in below explanation.

Step-by-step explanation:

According to the question, we have to find out 46+7

First, we need to add 6 and 7 by that we get the result 13.

Where, 3 will be the digit in once place of our answer.

And, we need to add 1 in 4, that is 5 by that we get the tenth place digit of our result. which is 5.

So, our complete answer is 53.

8 0

3 years ago

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Which best describes the relationship between the line that passes through the points (–6, –1) and (–11, 1) and the line that pa

yaroslaw [1]

The two are perpendicular to each other because the two slopes are negative reciprocals

(Y2 - Y1) / (X2 - X1)

First slope:
( 1 - (-1)) / (-11 - (-6))
2/-5

Second slope:
(-13 - (-8)) / (-5 - (-3))
-5/-2 or 5/2

You know when two aliens are perpendicular when you multiply the two slopes and get -1 as the product

-2/5 X 5/2 = -1

Thus the two lines are perpendicular to each other.

3 0

3 years ago

Read 2 more answers