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OlgaM077 [116]
3 years ago
9

How to solve algebraic equations with 2 variables

Mathematics
1 answer:
melisa1 [442]3 years ago
8 0
You re write the equation, so when the equations are added one of the variables are eliminated
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Find the limit
Lana71 [14]

Step-by-step explanation:

<h3>Appropriate Question :-</h3>

Find the limit

\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]

\large\underline{\sf{Solution-}}

Given expression is

\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]

On substituting directly x = 1, we get,

\rm \: = \: \sf \dfrac{1-2}{1 - 1}-\dfrac{1}{1 - 3 + 2}

\rm \: = \sf \: \: - \infty \: - \: \infty

which is indeterminant form.

Consider again,

\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]

can be rewritten as

\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]

\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]

\rm \: = \: \sf \: \dfrac{1 - 3}{1 \times (1 - 2)}

\rm \: = \: \sf \: \dfrac{ - 2}{ - 1}

\rm \: = \: \sf \boxed{2}

Hence,

\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}

\rule{190pt}{2pt}

7 0
2 years ago
Read 2 more answers
Please help me asap ​
Bezzdna [24]

Answer:

d

Step-by-step explanation:

cannot be a or c cause it has a negative sign in front of it causing it to reflect over y axis. Cannot be B cause it doesn't have two coefficients with X. I also graphed it.

5 0
3 years ago
What’s the answer for y= (x-2)^2 +2 {x&lt;4.5}
stealth61 [152]

Answer:

x<4.5

Step-by-step explanation:

y =(x-2)^2 +2 {x<4.5}

add the power and then divide by 2 you get 4.5

8 0
3 years ago
5. During the election for class president,
Alex Ar [27]

60 more students voted for Kevin

Step-by-step explanation:

Given

total students = 300

Voted for Jennifer = 40%

Voted for Kevin = 60%

We will find number of students for one of them and then will subtract from total to find the others.

So,

Students who voted for Jennifer:

= 40\%\ of\ 300\\=0.40*300\\=120\ students

Students who voted for Kevin

==Total\ students-Students\ who\ voted\ for\ Jennifer\\=300-120\\=180\ students

In order to calculate that how many more students voted for Kevin :

180-120 = 60

Hence,

60 more students voted for Kevin

Keywords: Percentage

Learn more about percentage at:

  • brainly.com/question/11007026
  • brainly.com/question/11207748

#LearnwithBrainly

4 0
3 years ago
Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade. Mrs. Benson has how many math assignmen
timofeeve [1]

Mrs. Benson has 184 math assignments left to grade.

<u>Step-by-step explanation:</u>

Here we have , Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade.We need to find Mrs. Benson has how many math assignments left to grade. Let's find out:

Let total Number of math assignments be x , So According to question 46 math assignments are graded & 80% are left i.e.

⇒ x = 46+\frac{80x}{100}

⇒ x -\frac{80x}{100}= 46

⇒ \frac{100x-80x}{100}= 46

⇒ \frac{20x}{100}= 46

⇒ \frac{x}{5}= 46

⇒ x=230

Now , Assignments left to grade is :

⇒ 230-46

⇒ 184

Therefore , Mrs. Benson has 184 math assignments left to grade.

4 0
3 years ago
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