$\log_{3}5\cdot\log_{25}9=\dfrac{1}{\log_{5}3}\cdot\log_{25}9=\dfrac{1}{\log_{5}3}\cdot\log_{5^2}9=\dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}9=\\\\\\=
\dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=\boxed{1}$

8 0

3 years ago

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Ana knows the perimeter of her backyard is 6x+14x. if the length of her yard is 2x+3x-7,what is the width of her backyard? answe

vlada-n [284]

Using the simple Perimeter formula we can set up our equation.
$p = 2l + 2w$
$6x + 14x = 2(2x + 3x - 7) + 2w$
$20x = 4x + 6x - 14 + 2w$
$10x = - 14 + 2w$
$10x + 14 = 2w$
$5x + 7 = w$
Therefore the width is 5x + 7.

3 0

4 years ago

a man can walk 5 miles in 6 hours. if his speed increased 50% how long would it take to walk 6 miles

____ [38]

Answer:

It would take him 4.8 hours to walk 6 miles

Explanation:

1- getting his old speed:

We are given that the man can walk 5 miles in 6 hours

Speed is distance/time

Therefore:

Old speed = 5/6 miles/hour

2- getting his new speed:

We are given that his speed increased by 50%

This means that:

New speed = old speed + (50% * old speed)

New speed = $\frac{5}{6} + 0.5(\frac{5}{6}) = \frac{5}{4}$ miles/hour

3- getting the time taken to walk 6 miles based on new speed:

$Speed = \frac{distance}{time}\\ \\ \frac{5}{4} = \frac{6}{time}\\ \\ 5*time = 6*4 = 24\\ \\ time = \frac{24}{5} = 4.8 hours$

Hope this helps :)

3 0

3 years ago