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stira [4]
3 years ago
15

In triangle FEG pointH is between points E and F Point J is between points F and G and HJ is parallel to EG EH equals 14 HF equa

ls 26 and FG equals 60 what is FJ

Mathematics
1 answer:
kozerog [31]3 years ago
7 0

Answer:

FJ=39\ units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

\frac{FE}{FH}=\frac{FG}{FJ}

we have

FE=HF+EH=26+14=40\ units

FH=HF=26\ units

FG=60\ units

substitute the given values

\frac{40}{26}=\frac{60}{FJ}

FJ=26(60)/40\\FJ=39\ units

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Jim has only dimes and nickels in his coin bank. He has 37 coins with a total value of $2.65.
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Answer:

21

Step-by-step explanation:

Let x represent the number of dimes and y represent the number of nickels.  The total number of coins is 37; this gives us the equation

x+y = 37

Each dime is worth ten cents, or 0.10, and each nickel is worth five cents, or 0.05.  The total amount of money is given by

0.10x+0.05y = 2.65

This gives us the system

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To solve this, we will use substitution.  We will isolate x in the first equation:

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x+y-y = 37-y

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3.70-0.05y-3.70 = 2.65-3.70

-0.05y = -1.05

Divide both sides by -0.05:

-0.05y/-0.05 = -1.05/-0.05

y = 21

There were 21 nickels.

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