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2 years ago

Please help simplify the following expression

Mathematics

1 answer:

sladkih [1.3K]2 years ago

6 0

Answer:

$7 m^{21}n^{66}p^{5}$

Step-by-step explanation:

Given expression:

$\dfrac{21m^{42}n^{82}p^{10}}{3m^{21}n^{16}p^{5}}$

Therefore:

$\implies \dfrac{21}{3} \cdot \dfrac{m^{42}}{m^{21}} \cdot \dfrac{n^{82}}{n^{16}} \cdot \dfrac{p^{10}}{p^5}$

Simplify the coefficient:

$\implies 7 \cdot \dfrac{m^{42}}{m^{21}} \cdot \dfrac{n^{82}}{n^{16}} \cdot \dfrac{p^{10}}{p^5}$

$\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies 7 \cdot m^{42-21} \cdot n^{82-16} \cdot p^{10-5}$

$\implies 7 \cdot m^{21} \cdot n^{66} \cdot p^{5}$

Therefore:

$\implies 7 m^{21}n^{66}p^{5}$

Learn more about laws of exponents here:

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3 years ago

Explain how you would estimate to subtract 189 from 643

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3 years ago

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Afirm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced

s2008m [1.1K]

Cost function, $C(x)=300+15x$

Revenue function, $R(x) = 30x$

Profit function, $P(x)=15x-300$

Break point $x=20$ .

Fixed cost $=$ $ $300$ .

Variable cost $=$ $ $15$ .

Price of item $=$ $ $30$ .

Let $x$ be the number of items produced and sold.

a) Cost function $=$ Fixed cost $+$ variable cost \times number of items

So, $C(x)=300+15x$

b) Revenue $=$ Price of an item $\times$ number of items

So, $R(x) = 30x$

c) Profit $=$ Revenue $-$ Cost

$P(x)=R(x)-C(x)$

$P(x)=30x-300-15x$

$P(x)=15x-300$

d) Break even point $R(x)=C(x)$

$30x=300+15x$

$30x-15x=300$

$15x=300$

$x=20$ .

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2 years ago

SOMEONE PLEASE HELP! THANK YOU

Andrew [12]

Answer:

arithmetic; common difference; 8

Step-by-step explanation:

Let's first define arithmetic and geometric sequences:

Arithmetic:

Arithmetic sequences are made up of successive terms that share a common difference. In other words, if the sequence is, say: a, b, c, d, then we know that: d - c = c - b = b - a

Geometric:

Geometric sequences are made up of successive terms that share a common ratio. In other words, if the sequence is, say: e, f, g, h, then we know that:

h/g = g/f = f/e (where the / denotes division)

Here, let's try applying the arithmetic sequence rule to the three terms:

2, 10, 18

18 - 10 = 8

10 - 2 = 8

Ah, we see that the common difference is indeed 8, so this is an arithmetic sequence.

Thus, the answer is: arithmetic; common difference; 8.

~ an aesthetics lover

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4 years ago

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Mrrafil [7]

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3 years ago

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