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2 years ago

Simplify the rational expression: x^2+13x+42/x^2+15x+56

Mathematics

1 answer:

ANTONII [103]2 years ago

8 0

Answer:

x+6/x+8

Step-by-step explanation:

First, factor out each of the expressions. You will use the AM method, where the last term is the factors multiplied together, and the middle term is the two added together. For the top, you would get (x+7) and (x+6) as your factors, and for the bottom you'd get (x+7) and (x+8). Based off of that, you can simplify your answer. The two (x+7)'s can cancel out, leaving you with a (x+6) over (x+8) as your answer.

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4 years ago

identify the expression which could represent the statement "the product of c and a factor not dependent on c

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X*c
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4 years ago

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Rina8888 [55]

Answer/Step-by-step explanation:

17. Slope = rise/run

rise = 5

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18. Slope = rise/run

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3 years ago

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:

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

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

Then, since distance cannot be negative, we need to take the positive value, so, the son's step is 0.6m or 60 cm.

Now, calculating the father's step, we have:

$FatherStep=SonStep+20cm\\\\FatherStep=60cm+20cm=80cm$

Hence, we have that the father's step is 80 cm.

Have a nice day!

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3 years ago

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Rainbow [258]

Answer:

the answer is the first and why did you delete my answer

Step-by-step explanation:

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