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Vlad1618 [11]
3 years ago
13

The extensions of the legs AB and CD of a trapezoid ABCD intersect at point E. Find the lengths of the altitude of △AED drawn to

the base AD, if BC=7cm, AD=21cm, and the length of an altitude of a trapezoid is 3cm.

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

let's call G the intersection point of EF & BC.

according to the thales' theorem:

\frac{eg}{ef}  =  \frac{bc}{ad}

and EF= EG+GF=EG+3

\frac{eg}{eg + 3}  =  \frac{7}{21}

21eg = 7eg + 21

14eg = 21

eg =  \frac{21}{14}  =  \frac{3}{2}  = 1.5

length of the altitude of △AED=EF

EF=EG+GF=1.5+3=4.5

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3 years ago
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6 0
3 years ago
I don’t get it I need help solving this math problem I
harkovskaia [24]

Answer:

Step-by-step explanation:

you know the total angle is 180° from A to D

and you know that ∠BEC is 90°

also you are told that ∠CED is 18°

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so just put that all together

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now solve for X

180-90-18=4x

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so now you know X

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6 0
2 years ago
Two landscapers must mow a rectangular lawn that measures 100 feet by 200 feet. Each wants to mow no more than half of the lawn.
Citrus2011 [14]

The total area of the complete lawn is (100-ft x 200-ft) = 20,000 ft².
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When you think about it ... massage it and roll it around in your
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you realize that if he starts along the length of the field, then with
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First lap:
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Second lap:
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       (100 - 6) = 94
       (200 - 6) = 194
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Third lap:
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       (200 - 10) = 190
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These are the lengths of each strip.  They're 2-ft wide, so the area
of each one is (2 x the length). 

I expected to be able to see a pattern developing, but my brain cells
are too fatigued and I don't see it.  So I'll just keep going for another
lap, then add up all the areas and see how close he is:

Fourth lap:
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So far, after four laps around the yard, the 16 lengths add up to
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at least four more laps ... probably more, because they're getting smaller
all the time, so each lap contributes less area than the last one did.

Hey ! Maybe that's the key to the approximate pattern !

Each lap around the yard mows a 2-ft strip along the length ... twice ...
and a 2-ft strip along the width ... twice.  (Approximately.)  So the area
that gets mowed around each lap is (2-ft) x (the perimeter of the rectangle),
(approximately), and then the NEXT lap is a rectangle with 4-ft less length
and 4-ft less width.

So now we have rectangles measuring

         (200 x 100),  (196 x 96),  (192 x 92),  (188 x 88),  (184 x 84) ... etc.

and the areas of their rectangular strips are
           1200-ft², 1168-ft², 1136-ft², 1104-ft², 1072-ft² ... etc.

==> I see that the areas are decreasing by 32-ft² each lap.
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How much area do we have now:

             After 9 laps,    Area =   9,648-ft²
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And there you are ... Somewhere during the 10th lap, he'll need to
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There must still be an easier way to do it.  For now, however, I'll leave it
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5 0
3 years ago
Use the remainder theorem to divide 5x^2+9x-2 by x+3. What is the remainder
marishachu [46]

Answer:

16

Step-by-step explanation:

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f(x)=5x^2+9x-2

Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).

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f(-3) = 5(-3)^2 +9(-3) -2

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        = 16 !

7 0
2 years ago
Read 2 more answers
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