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4 years ago

6

Given the linear equation 2x + y = 6, perform the necessary operations to put the equation into the proper general form. Explain

in complete sentences how you knew that the equation was in the proper general form. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the entire process for establishing the general form of the equation and the general form.

1 answer:

likoan [24]4 years ago

3 0

Step-by-step explanation:

The general equation is y = mx + c...

The given equation is 2x + y = 6

Firstly, move everything on the left except the y to the right.i.e.

y = 6 - 2x

Secondly, rearrange the values on the right to look just like the general equation.

y = -2x + 6

The equation is now in proper general form because it matches the format laid down.

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3 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

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$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

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Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

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$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

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$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

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$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

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$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

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