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2 years ago

5

A certain colony of bacteria triples in length every 10 minutes, its length is now 1 millimeter. How long will it be in 40 minut

es?

1 answer:

Law Incorporation [45]2 years ago

3 0

Answer:

81 mm

Step-by-step explanation:

Now: 1 mm

In 10 minutes: 3 * 1 mm = 3 mm

In 20 minutes: 3 * 3 mm = 9 mm

In 30 minutes: 3 * 9 mm = 27 mm

In 40 minutes: 3 * 27 mm = 81 mm

Answer: 81 mm

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(−5)3x7(yz)4 / (3)2x2y8z2

g100num [7]

Answer:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

Step-by-step explanation:

Given:

The expression to simplify is given as:

$\frac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}$

In order to simplify this, we have to use the law of indices.

1. $(ab)^m=a^mb^m$

So, $(yz)^4=y^4z^4$

Substitute this value in the above expression. This gives,

$=\dfrac{(-5)3x^7y^4z^4}{(3)2x^2y^8z^2}\\\\\\=\dfrac{-15x^7y^4z^4}{6x^2y^8z^2}......(-5\times 3=15\ and\ 3\times 2=6)$

Now, we use another law of indices.

2. $\frac{a^m}{a^n}=a^{m-n}$

So, $\frac{x^7}{x^2}=x^{7-2}=x^5,\frac{y^4}{y^8}=y^{4-8}=y^{-4}, \frac{z^4}{z^2}=z^{4-2}=z^2$

Substitute these values in the above expression. This gives,

$=\frac{-15}{6}\times x^5\times y^{-4}\times z^2\\\\=\frac{-5x^5y^{-4}z^2}{2}$

Finally, we further simplify it using the law $a^{-m}=\frac{1}{a^m}$

So, $y^{-4}=\frac{1}{y^4}$

Therefore, the given expression is simplified as:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

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2 years ago

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2 years ago

Sophie [7]

<u>Part 1</u>

<u /> $(f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1$

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is $\boxed{[0, \infty)}$

<u>Part 2</u>

<u /> $(g \circ f)(x)=g(4x+1)=\sqrt{4x+1}$

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,

$4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}$

Thus, the domain in interval notation is $\boxed{\left[-\frac{1}{4}, \infty)}$

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1 year ago

kiyo's art class was studying symmetry balance and line of symmetry. kiyo's drew this cross shape polygon. how many lines of sym

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Answer:

4

Step-by-step explanation:

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2 years ago

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dolores and four friends went to a buffet dinner.The total cost was at most $130 including the $20 dollar tip they left.How much

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So the actual meal was at most 130 dollars they paid minus the 20 dolars tip: 130-20=110 dollars.

it was 5 people: Dolores+5 friends, who presumably all paid the same (buffet).

then we have to divide the 110 among the 5 people: it's 110/5=22

so each of them paid at most 22 dollars:

x (the amount they paid)≤22

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3 years ago