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3 years ago

7

A tire shop had to fill 2 1/2 tires with air. It took a small air compressor 2 1/2 seconds to fill them up. How long would it ta

ke to fill 8 tires?

1 answer:

Delicious77 [7]3 years ago

4 0

Answer:

8 seconds

Step-by-step explanation:

2 1/2 ÷ 2 1/2=1

1*1=1

1*8=8

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Step-by-step explanation:

In this problem, we can see a pattern. If she triples the number of beads in each of the next strings, that means that we just take the last number and multiply by 3. If the first string uses 3, then:

The second uses 9, 3 * 3 = 9

The third uses 27, 9 * 3 = 27

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HACTEHA [7]

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = \frac{16}{9}$

4ˣ⁻¹ = 49 / 4

<h3>How to simplify an expression?</h3>

The expressions can be simplified as follows;

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} }$

Hence,

$(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} }$

Therefore,

$(\frac{4}{3} )^{2(\frac{2}{3} )}.(\frac{4}{3} ) ^{\frac{5}{3} } = (\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} }$

Finally,

$(\frac{4}{3} )^{\frac{4}{3} } .(\frac{4}{3} )^{\frac{5}{3} } = (\frac{4}{3} )^{3}$

$(\frac{4}{3} )^{3} = \frac{16}{9}$

2ˣ = 7

4ˣ⁻¹ = 2²⁽ˣ⁻¹⁾ = 2²ˣ ⁻ ² = 2²ˣ / 2² = (2ˣ)² / 2²

Therefore,

(2ˣ)² / 2² = 7² / 2² = 49 / 4

Hence,

4ˣ⁻¹ = 49 / 4

Finally, the $(\frac{16}{9})^{\frac{2}{3} }. (\frac{4}{3} ) ^{\frac{5}{3} }$ is equal to $\frac{16}{9}$ and for the second part 4ˣ⁻¹ = 49 / 4

learn more on simplification here: brainly.com/question/17513857

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