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4 years ago

6

Brian gave 1/4 of his stickers to Pete and 20 stickers to Lily. He then had 1/3 of his stickers left. How many stickers did he h

ave at First?

1 answer:

Oduvanchick [21]4 years ago

8 0

Find a common denominator first.
P3/12. + 5/12
4/12 left

48 stickers

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find the circumference and the area of the circle with the radius 9m use the value 3.14 for it do not round your answer be sure

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Explanation:

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$\begin{gathered} A=\pi r^2 \\ C=2\pi r \end{gathered}$

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1 year ago

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3 years ago

Find the obtuse angle between the following pair of straight lines.

ioda

Given:

$y=-2$

$y=\sqrt{3}x-1$

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

The given equations are

$y=0x-2$

$y=\sqrt{3}x-1$

On comparing these equations with (i), we get

$m_1=0$

$m_2=\sqrt{3}$

Angle between two lines whose slopes are $m_1\text{ and }m_2$ is

$\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|$

Putting $m_1=0$ and $m_2=\sqrt{3}$ , we get

$\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|$

$\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|$

$\tan \theta=\pm \sqrt{3}$

Now,

$\tan \theta= \sqrt{3}$ and $\tan \theta=-\sqrt{3}$

$\tan \theta= \tan 60^\circ$ and $\tan \theta=\tan (180^\circ-60^\circ)$

$\theta= 60^\circ$ and $\theta=120^\circ$

$120>90$ , so it is an obtuse angle and $60$ , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

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3 years ago