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Amanda [17]
3 years ago
15

What is the quotient in simplified form ? Need help please

Mathematics
1 answer:
Gre4nikov [31]3 years ago
8 0

Answer:

  -\dfrac{4a^{12}b^8}{5}

Step-by-step explanation:

The applicable rules of exponents are ...

  \dfrac{1}{a^{-b}}=a^b\\\\a^ba^c=a^{b+c}

Your ratio simplifies to ...

  \dfrac{-8a^8b^{-2}}{10a^{-4}b^{-10}}=-\dfrac{4}{5}a^{8-(-4)}b^{-2-(-10)}\\\\=-\dfrac{4a^{12}b^8}{5}

_____

Please note that simplifying the constants, -8/10 to -4/5, eliminates half the answer choices. Since exponents are only multiplied when a power is raised to a power, you can pretty much eliminate the second choice as being unreasonable. ((a^b)^c = a^(bc))

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Answer: Choice A) M = 0.25n + 100

=============================================================

Explanation:

For now, I'll treat n as x, and M as y.

In other words,

  • x = number of CDs
  • y = total mass in kg

Let's select two points from this graph. I'll pick (200,150) and (400,200)

The slope of the line through those points is

m = (y2-y1)/(x2-x1)

m = (200-150)/(400-200)

m = 50/200

m = 0.25

Now we'll use the point (x,y) = (200,150) along with that slope value to find the y intercept b

y = mx+b

150 = 0.25*200+b

150 = 50+b

150-50 = b

100 = b

b = 100

You could also use (x,y) = (400,200) and you should get the same b value.

In fact, any other point from this graph works as well.

------------------------------

Since m = 0.25 and b = 100, we go from y = mx+b to y = 0.25x+100

This then translates over to M = 0.25n + 100 which is choice A

To help verify this, let's say we plugged in n = 100

M = 0.25*n + 100

M = 0.25*100 + 100

M = 25 + 100

M = 125

Which is confirmed by what the graph shows. I'll let you check the other points as well.

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3 years ago
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Step-by-step explanation:

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Answer:

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3

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Step-by-step explanation: is this the answer?

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