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3 years ago

How many fractions are equivalent to 4/5? explain

1 answer:

7 0

There are several fractions that are equivalent to 4/5. Some are 8/10, 80/100, 800/1000. They all equal the same decimal: 0.8

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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

State whether the system is consistent and independent, consistent and dependent or inconsistent.

user100 [1]

Answer:

The correct option is 1.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

$x+3y=18$ .... (1)

$-x+2y=7$ ..... (2)

Add both equations.

$x+3y-x+2y=18+7$

$5y=25$

$y=5$

Substitute this value in equation (1).

$x+3(5)=18$

$x+15=18$

$x=3$

The system of equations has only one solution, i.e.,(3,5).

Therefore the given system is consistent and independent. Option 1 is correct.

7 0

2 years ago

Read 2 more answers

Stella wants to buy a remote control helicopter. The one she wants costs $120.

aalyn [17]

.45 * 120 = 54

.072 * 54 = 3.888

54 + 3.888 = 57.888= $57.89

5 0

1 year ago

Read 2 more answers

360km is 24% of what km

lawyer [7]

Let required distance be x km
24x
---- = 360
100

x = (100*360) / 24 = 1500 km Answer

7 0

3 years ago

What is 5467.8 in scientific notation??

adoni [48]

Answer:

5.47 x 10^3

Step-by-step explanation:

6 0

3 years ago