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Tcecarenko [31]
2 years ago
8

A triangular course for a canoe race is marked with buoys. The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg

is 2/5 mi. How long is the race?
Mathematics
1 answer:
balu736 [363]2 years ago
7 0
<h2>The race is 1.2 miles long</h2>

Step-by-step explanation:

The first leg is 3/10 mi, the second leg is 1/2 mi, and the third leg is 2/5 mi.

\texttt{Length of first leg = }\frac{3}{10}miles\\\\\texttt{Length of second leg = }\frac{1}{2}miles\\\\\texttt{Length of third leg = }\frac{2}{5}miles

Now we need to find length of race

       \texttt{Total length = }\frac{3}{10}+\frac{1}{2}+\frac{2}{5}\\\\\texttt{Total length = }\frac{3}{10}+\frac{5}{10}+\frac{4}{10}\\\\\texttt{Total length = }\frac{3+5+4}{10}\\\\\texttt{Total length = }\frac{12}{10}\\\\\texttt{Total length = }1.2miles

The race is 1.2 miles long

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*In ∆ABC, on the extension of the side BC , draw a line segment CD ≅ CA . Draw the segment AD . The line segment CE is the angle
Leya [2.2K]

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Step-by-step explanation:

In ∆ABC

  • On the extension of the side BC , draw a line segment CD ≅ CA
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  • The line segment CE is the angle bisector of ∠ACB
  • The line segment CF is the median towards AD in ∆ ACD

We want to prove that CF ⊥ CE

Look to the attached figure

In Δ ABC

∵ CE is the bisector of angle ACB

∴ ∠ACE ≅ ∠BCE

In Δ ACD

∵ CA = CD

∴ Δ ACD is an isosceles triangle

∵ AD is the median towards AD

- In any isosceles triangle the median from a vertex to its opposite

  side bisects this vertex

∴ AD bisects ∠ACD

∴ ∠ACF ≅ ∠DCF

∵ BCD is a straight segment

∵ CE , CA , CF are drawn from point C

∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°

∵ m∠ACE ≅ m∠BCE

∵ m∠ACF ≅ m∠DCF

- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF

∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°

∴ 2 m∠ACE + 2 m∠ACF = 180°

- Divide all terms by 2

∴ m∠ACE + m∠ACF = 90°

∴ EC ⊥ CF

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Learn more:

You can learn more about perpendicular lines in brainly.com/question/11223427

#LearnwithBrainly

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3 years ago
Seven more then 3 rimes a number is 49
NikAS [45]
7 <span> more than 3 times a number </span>
<span>more than is code for + </span>
<span>times is multiply </span>
<span>so 7+3n=31 </span>

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<span>3n=24 </span>
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6 0
3 years ago
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A space shuttle travels at 2.6 x 10,000 feet per second. An hour is 3.6 x 1,000 seconds. This expression can be used to find the
guapka [62]

Answer:

7.22 feet

Step-by-step explanation:

From the question,

s = d/t................. Equation 1

Where s = speed of the space shuttle, d = distance traveled by the shuttle in an hour, t = time taken to travel the distance

make d the subject of the equation,

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Given: s = 2.6×10000 feet per seconds, t = 1 hour =  3.6×1000 seconds.

Substitute these values into equation 2

d = (2.6×10000)/(3.6×1000)

d = 26000/3600

d = 7.22 feet.

Hence the shuttle travels 7.22 feet in an hour

6 0
2 years ago
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