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gayaneshka [121]
3 years ago
10

PLEASE HELP (30 POINTS) Solve the rational equation x/3 = x^2/x + 5 , and check for extraneous solutions.

Mathematics
1 answer:
anygoal [31]3 years ago
8 0

Option C: x=0 and x=\frac{5}{2} are the solutions.

Explanation:

The equation is \frac{x}{3} =\frac{x^{2} }{x+5}

We shall determine the value of x, by simplifying the equation.

$\begin{aligned} x(x+5) &=3 x^{2} \\ x^{2}+5 x &=3 x^{2} \\ 2 x^{2}-5 x &=0 \\ x(2 x-5) &=0 \end{aligned}$

Thus, x=0 and x=\frac{5}{2} are the solutions.

Now, let us check whether the solutions are extraneous solutions.

Let us substitute x=0 in the original equation to check whether both sides of the equation are equal.

\begin{aligned}&\frac{0}{3}=\frac{0^{2}}{0+5}\\&0=\frac{0}{5}\\&0=0\end{aligned}

Thus, both sides of the equation are equal.

Hence x=0 is a true solution.

Now, Let us substitute x=\frac{5}{2} in the original equation to check whether both sides of the equation are equal.

\begin{aligned}\frac{\left(\frac{5}{2}\right)}{3} &=\frac{\left(\frac{5}{2}\right)^{2}}{\left(\frac{5}{2}\right)+5} \\\frac{5}{6} &=\frac{\left(\frac{25}{4}\right)}{\left(\frac{15}{2}\right)} \\\frac{5}{6} &=\frac{5}{6}\end{aligned}

Thus, both sides of the equation are equal.

Hence, x=\frac{5}{2} is a true solution.

Thus, solutions are not extraneous.

Hence, Option C is the correct answer.

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Can someone please explain how to solve this problem(31)
pogonyaev

Answer:

  (-1.92, 1.08)

Step-by-step explanation:

The <em>incenter</em> is the center of the largest circle that can be inscribed in the triangle. That circle is called the <em>incircle</em>. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the <em>inradius</em> (the radius of the incircle), is found from a simple formula:

  r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs

In your triangle, the inradius is ...

  r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452

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4 0
3 years ago
What is the inverse of the function f(x) = x +3?
KatRina [158]
Next time please add answer choices 

f(x) = y = x+3, Consider y=x+3. You just switch x and y:
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Answer:

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The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

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  • Grey colored portion = {3}

  • White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

  • X = Event that wheel stops on a white slice

  • P(X) = number of white slices ÷ total number of slices

  • P(X) = 9 / 10 = 0.9

  • P(not X) = 1 - P(X)

  • P(not X) = 1 - 0.9 = 0.1

Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

Learn more :brainly.com/question/18153040

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