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3 years ago

Represent2/3on the number line.

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

5 0

Answer:

2/3 lies between 0 and 1 on the number line.

Step-by-step explanation:

2/3 is a positive rational number, and it is known that 2/3 is less than 1 and greater than 0.

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Simplify 0.95x-9-1/2x(36-18y)-0.25(-3x+4.8)

iris [78.8K]

Answer: 9xy−16.3x−10.2

Step-by-step explanation:

Distribute:

=0.95x+−9+9xy+−18x+(−0.25)(−3x)+(−0.25)(4.8)

=0.95x+−9+9xy+−18x+0.75x+−1.2

Combine Like Terms:

=0.95x+−9+9xy+−18x+0.75x+−1.2

=(9xy)+(0.95x+−18x+0.75x)+(−9+−1.2)

=9xy+−16.3x+−10.2

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3 years ago

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

anygoal [31]

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.

8 0

3 years ago

Represent2/3on the number line.​

Represent2/3on the number line.