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3 years ago

Use substitution to solve the linear system of equations.

Mathematics

1 answer:

Ne4ueva [31]3 years ago

6 0

Answer:

Step-by-step explanation: infinitely many solutions (please give brainliest)

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A classmate simplified a rational expression below

lara31 [8.8K]

<h2>Part a) </h2><h2>Explain the error in this simplification.</h2>

Given the simplified expression

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

$1-2\left(x+2\right)=\left(x+1\right)\left(x-2\right)$

$\:1-2x-4=x^2-x-2$

$-2x-3=x^2-x-2\:\:$

$0=x^2-2x-2\:\:$

$0=\left(x-1\right)\left(x-1\right)$

$x=1$

Identifying the Main Error

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

$1-2\left(x+2\right)=\left(x+1\right)\left(x-2\right)$ ← ERROR Starts here

Here is the Explanation of the Error

$\mathrm{The\:equation\:should\:have\:been\:Multiplied\:by\:LCM=}\left(x-2\right)\left(x+2\right)$ . In your case you wrongly multiply the equation.

CORRECTION

HERE IS HOW YOU SHOULD HAVE MULTIPLIED BY LCM = (x-2)(x+2):

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

$1\cdot \left(x-2\right)\left(x+2\right)-\frac{2}{x-2}\left(x-2\right)\left(x+2\right)=\frac{x+1}{x+2}\left(x-2\right)\left(x+2\right)$

$\left(x-2\right)\left(x+2\right)-2\left(x+2\right)=\left(x+1\right)\left(x-2\right)$

<h2>Part b) </h2><h2>Show your work as you correct the error</h2>

Here is the complete correction of the error.

Considering the expression

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

$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x-2,\:x+2:\quad \left(x-2\right)\left(x+2\right)$

$1\cdot \left(x-2\right)\left(x+2\right)-\frac{2}{x-2}\left(x-2\right)\left(x+2\right)=\frac{x+1}{x+2}\left(x-2\right)\left(x+2\right)$

$\left(x-2\right)\left(x+2\right)-2\left(x+2\right)=\left(x+1\right)\left(x-2\right)$

$x^2-2x-8=x^2-x-2$

$x^2-2x-8+8=x^2-x-2+8$

$x^2-2x=x^2-x+6$

$-x=6$

$\frac{-x}{-1}=\frac{6}{-1}$

$x=-6$

3 0

3 years ago

The volume of a cone is 225 cubic inches. The diameter is 15 inches. What is the height of the cone?

mrs_skeptik [129]

its answer is No.C {4 inches}

4 0

3 years ago

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If each person takes up 2.25 square feet of space, how many people can fit into an area that is 15 feet by 30 feet?

Nimfa-mama [501]

15x30= 450 sq ft
450/2.25= 200
so 200 people can fit in an area of 15x30

5 0

3 years ago

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Factorise using identity 4y^2 - 12yz+9z^2

Andrew [12]

Step-by-step explanation:

Identity used  :

$\bold{ ({y}^{2} + {z}^{2}) = {y}^{2} + 2yz + {z}^{2} }$

$\implies \: {(2y)}^{2} - 2.2y.3z + {(3z)}^{2}$

so we got :

y = 2

z = 3

${ \pink{ \bold{ \boxed{answer = (2y + 3z) {}^{2} }}}}$

 

8 0

4 years ago

The area of a square with side length 3 cm is Cm2

mr_godi [17]

6 is the area of the square

3 0

3 years ago

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