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yulyashka [42]
3 years ago
14

Melody and khaleef are starting new books in their literature classes.Melodys book has 265 pgs and khaleef book has 424 pgs.So f

ar,Melody has read 2/5 of total pages in her book.What fraction of khaleef book must he read on prde5to read the same number of pgs as melody has read so far? Answer in simplest form
Mathematics
1 answer:
sladkih [1.3K]3 years ago
8 0

Answer:

1/4

Step-by-step explanation:

We want ...

... (Melody's fraction) × (Melody's pages) = (Khaleef's fraction) × (Khaleef's pages)

Filling in the numbers, this is ...

... (2/5)×265 = (Khaleef's fraction)×424

Dividing by 424, we have ...

... Khaleef's fraction = (2/5)×(265/464) = (2/5)×(5/8) = 2/8 = 1/4

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Answer:

7 )

x =  \frac{3\sqrt{2} }{2}

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8 )

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Step-by-step explanation:

7  )                                 8)

In Δ ABC                                      In Δ XYZ            

∠ C = 45°                                          ∠ X = 60°

∠ A = 90°                                           ∠ Y = 90°

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Solution:

We Know

In Δ ABC

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∴  Δ ABC is an Isosceles Triangle

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\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2}  }{2}\\\\y= 3

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30°  . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}

\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\  y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}

Now,

\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}

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