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satela [25.4K]
3 years ago
14

Your goal is to have an emergency fund equal to 3 months living expenses. Your living expenses are $700 a month. Your take-home

pay per month is $1,100, and you plan to put 10% toward your emergency fund each month. How long will it take you to reach your goal?
Mathematics
1 answer:
anyanavicka [17]3 years ago
6 0
6.4 months Because 10% of $1,100 is $110 

multiply 110 by 6.4 and you get 704 

so 6.4 months
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In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,
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Answer:

The answer is below

Step-by-step explanation:

In triangle DEF, ∠D = 30°, ∠F = 60° and EF = 6. Find DE + DF.

Solution:

A triangle is a polygon with three sides. There are different types of triangles such as isosceles triangle, scalene triangle equilateral triangle, right angled triangle.

In triangle DEF:

∠D + ∠E + ∠F = 180° (sum of angles in a triangle)

30 + ∠E + 60 = 180

∠E + 90 = 180

∠E = 180 - 90

∠E = 90°

This is a right angled triangle since one angle = 90° (∠E).

Using sine rule:

\frac{|EF|}{sin(D)}=\frac{|DE|}{sin(F)}  \\\\\frac{6}{sin(30)}=\frac{|DE|}{sin(60)}  \\\\|DE|=10.39\\\\\frac{|EF|}{sin(D)}=\frac{|DF|}{sin(E)}  \\\\\frac{6}{sin(30)}=\frac{|DF|}{sin(90)}  \\\\|DF|=12\\\\

Hence DE + DF = 12 + 10.39 = 22.39

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If the shape is the same, but the size is different, <em>dilation is involved</em>. There may be other transformations that are also involved (such as rotation, translation, or reflection), so MNPQ may or may not be a straight dilation of M'N'P'Q'.

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Translation and dilation can sometimes be combined to a dilation about a point that is not the origin. Reflection might be accommodated by using a negative dilation factor. However, rotation cannot be accomplished using dilation alone.

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Answer:

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Answer:

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