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3 years ago

9

A cyclist rides her bike at a speed of 18 kilometers per hour. What is the sped in kilometers per minute? How many kilometers wi

ll the cyclist travel in 10 minutes? Do not round around your answer.
Speed:
Distance traveled in 10 minutes:

1 answer:

Alexeev081 [22]3 years ago

6 0

Answer:

speed: .3 kilometers a minute. Distance traveled in 10 minutes: 3 kilometers

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4 years ago

Which of these choices show a pair if equivelent expressions? Chack all that apply

Gwar [14]

Answer:

A. $(\sqrt[3]{125})^9\ and\ (125)^{\frac{9}{3}}$

D. $8^{\frac{9}{2}}\ and\ (\sqrt{8})^9$

Step-by-step explanation:

Equivalent expressions are those expressions that simplify to same form.

Now, let us check each of the given options.

Option A:

$(\sqrt[3]{125})^9\ and\ (125)^{\frac{9}{3}}$

We know that,

$\sqrt[n]{x} =x^{\frac{1}{n}}$

Therefore, $\sqrt[3]{125} =(125)^{\frac{1}{3}}$

Thus the first expression becomes;

$((125)^{\frac{1}{3}})^9$

Now, using law of indices $(a^m)^n=a^{m\times n}$ , we get

$((125)^{\frac{1}{3}})^9=((125))^{\frac{1}{3}\times 9}=((125))^{\frac{9}{3}$

Therefore, $(\sqrt[3]{125})^9\ and\ (125)^{\frac{9}{3}}$ are equivalent.

Option B:

$12^{\frac{2}{7}}\ and\ (\sqrt{12})^7$

Consider the second expression $(\sqrt{12})^7$

We know that,

$\sqrt x=x^{\frac{1}{2}}$

$(\sqrt{12})^7=((12)^{\frac{1}{2}})^7=(12)^{\frac{1}{2}\times 7}=(12)^{\frac{7}{2}}$

Therefore, $12^{\frac{2}{7}} \ne (12)^{\frac{7}{2}}$ . Hence, the expressions $12^{\frac{2}{7}}\ and\ (\sqrt{12})^7$ are not equivalent.

Option C:

$4^{\frac{1}{5}}\ and\ (\sqrt 4)^5$

We know that,

$x^{\frac{1}{n}}=\sqrt[n]{x}$

Therefore, $4^{\frac{1}{5}}=\sqrt[5]{4}$

Now, $\sqrt[5]{4}\ne (\sqrt 4)^5$

Therefore, the expressions $4^{\frac{1}{5}}\ and\ (\sqrt 4)^5$ are not equivalent.

Option D:

$8^{\frac{9}{2} }\ and\ (\sqrt 8)^9$

Using law of indices $a^{m\times n}=(a^m)^n$ , we get

$8^{\frac{9}{2} }=(8^{\frac{1}{2}})^9$

Now, we know that, $x^{\frac{1}{2}}=\sqrt x$

So, $(8^{\frac{1}{2}})^9=(\sqrt8)^9$

Therefore, $8^{\frac{9}{2} }\ and\ (\sqrt 8)^9$ are equivalent.

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3 years ago