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Mathematics

2 answers:

PilotLPTM [1.2K]3 years ago

8 0

In a right triangle, one angle is equal to 90 degrees while the sum of the other two angles are also 90 degrees. In this case, x is a right angle, so it equals 90 degrees. We know that one of the other angles is 47 while the second is y. So, y+47=90. To find y, we subtract 47 from 90, which is 43 degrees. y=43 degrees.

chubhunter [2.5K]3 years ago

6 0

<span>90+47=137 X is a right angle so it is going to equal 90 that is where the 90 came from.

180-137=43 to find y we have to subtract 180 (the sum of all triangles) by the sum of x and 47. Which ends up being 43.
X= 90
Y= 43</span>

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A father and his son walked 240 meters. During this trip, the father made 100 fewer steps than did his son. Find the distance ea

Alexxandr [17]

<h2>Hello!</h2>

The answer is:

The father's step is 80 cm

The son's step is 60 cm.

To solve the problem, we need to write equations in order to create a relation between the father's and son's steps, and the distance covered by them.

We know thay they covered 240 meters, and the father's step is 20 cm (0.2m)greater than his son's step, so, we can write the following relation:

$NumberOfSteps_{Son}=\frac{240m}{x}$

and,

$NumberOfSteps_{Father}=\frac{240m}{x+0.2m}$

Now, if the know that the father made 100 fewer steps than his son, we have:

$NumberOfSteps_{Son}-100=\frac{240m}{x+0.2m}$

Then, substituting the first equation into the second equation, we have:

$\frac{240m}{x}-\frac{240m}{x+0.2m}=100\\\\\frac{240m(x+0.2m)-240mx}{x(x+0.2m)}=100\\\\240mx+0.2m*240m-240mx=(x)(x+0.2m)*100\\\\48m^{2}=100*(x^{2}+0.2mx)=100x^{2} +20mx\\\\48m^{2}=100x^{2}+20mx\\\\100x^{2}+20mx-48m^{2}$

We have a quadratic equation:

$100x^{2}+20mx-48m^{2}=0$

Where,

$a=100\\b=20\\c=-48$

So, solving it applying the quadratic formula, we have:

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}$

$\frac{-20+-\sqrt{20^{2} -4*100*-48} }{2*100}=\frac{-20+-\sqrt{400+19200} }{200}\\\\\frac{-20+-\sqrt{400+19200} }{200}=\frac{-20+-\sqrt{19600} }{200}\\\\\frac{-20+-\sqrt{19600} }{200}=\frac{-20+-(140)}{200}\\\\x_{1}=\frac{-20+140}{200}=0.6\\\\x_{2}=\frac{-20-140}{200}=-0.8$