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3 years ago

Question 5 of 10

Mathematics

2 answers:

Temka [501]3 years ago

4 0

Answer:

8 units

Step-by-step explanation:

just took

Irina18 [472]3 years ago

3 0

Answer:

8 units

Step-by-step explanation:

due to math i conclude 8 units

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Which statement best reflects the solution(s) of the equation?

Inessa [10]

x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ and find values of x.

Solving:

Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)

Multiply the entire equation with x(x-1)

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0$

Now, factoring the term:

$x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2$

The values of x are x=1 and x=2

Checking for extraneous roots:

Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.

If we put x=1 in the equation, $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ the denominator becomes zero i.e

$\frac{1}{1-1}+\frac{2}{1}=\frac{1}{1-1}\\\frac{1}{0}+2=\frac{1}{0}$

which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.

If we put x=2 in the equation,

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$

$\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2$

So, x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Keywords: Solving Equations and checking extraneous solution

Learn more about Solving Equations and checking extraneous solution at:

#learnwithBrainly

5 0

4 years ago

Solve for the width in the formula for the area of a triangle

zmey [24]

Answer: $\frac{2A}{h} = w$

Step-by-step explanation:

The formula for area of a triangle is $A = wh\frac{1}{2}$

Now we have to isolate for w.

First multiply by the 2 which is the reciprocal of 1/2 to cancel it out.

$2A = wh\\$

Now divide by h to isolate w.

$\frac{2A}{h} = w$

4 0

3 years ago

What is the probability of drawing a 3 or a 4 or a heart from a deck of cards?

Effectus [21]

$\Omega=\{2\spadesuit;\ 3\spadesuit;...;A\spadesuit;2\heartsuit ;\ 3\heartsuit;...;A\heartsuit;\ 2\diamondsuit;\ 3\diamondsuit;...;A\diamondsuit;\ 2\clubsuit;\ 3\clubsuit;...;A\clubsuit\}\\\\|\Omega|=52\\\\A=\{3\spadesuit;\ 4\spadesuit;\ 3\diamondsuit;\ 4\diamondsuit;\ 3\clubsuit;\ 4\clubsuit;\ 2\heartsuit;\ 3\heartsuit;\ 4\heartsuit;...;A\heartsuit\}\\\\|A|=2+2+2+13=19\\\\P(A)=\dfrac{|A|}{|\Omega|}\to P(A)=\dfrac{19}{52}$

$Answer:\ \dfrac{19}{52}$

5 0

4 years ago

62 strings of orange lights and 22 strings of yellow lights were used in the house each string of lights has 36 bulbs how many b

Allisa [31]

62 + 22 = 84 total light strings.

36 bulbs/string multiplied by 84 light strings = 3,024 total light bulbs

5 0

3 years ago

The Sum of twice a number and 5 is at most 15. What are the possible values for the number?

NISA [10]

Let's call that number x, twice the number will be 2x, sum of it and 5 is, 2x+5. So if this expression is at most 15, it means, it can be only less than 15 and equal to 15. Let's show this as an inequality.

$2x+5\le 15$

Let's solve.

$2x+5\le 15\\ \\ 2x\le 15-5\\ \\ 2x\le 10\\ \\ x\le \frac { 10 }{ 2 } \\ \\ x\le 5$

$x\quad \in \quad \left[ -\infty ,5 \right]$

If the number is a natural number. The values it can take is, $x\quad \in \quad \left[ 0,1,2,3,4,5 \right]$

6 0

4 years ago

Read 2 more answers