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postnew [5]
3 years ago
7

What value of g makes the equation true? (x+7)(x-4)=x²+gx-28

Mathematics
1 answer:
defon3 years ago
6 0

Answer:

g=3

Step-by-step explanation:

multiply x with x-4 and +7 with x-4 to open the brackets

x^2 - 4x + 7x - 28 = x^2 +gx - 28

x^2 + 3x - 28 = x^2 + gx -28

x^2 - x^2 + 3x -28 + 28 = gx

gx is kept alone on the other side because we have to find value of g

cancel out +x^2 -x^2 and +28 -28

we ll be left with

3x = gx

divide both sides by x

3x/x = gx/x

cancel out x in the numerators with the x in the denominators

3 = g

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(1) Answer : (x^2 - 6x + 9) + (y^2- 4y + 4) = 3 + (9 + 4)

Step 1: x^2 - 6x + y^2 - 4y = 3

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In completing the square method we take coefficient of x and divide by 2 and the square it . Then add it on both sides

The coefficient of x is -6. \frac{-6}{2} = (-3)^2 = 9

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Step : (x^2- 6x + 9) + (y^2 - 4y + 4) = 3 +9 + 4

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To find center and radius we write the equation in the form of

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Center is (-3,3) and radius = 4

(c) Step 1: x^2 + 8x + y^2 -  6y = 11

Step 2: (x^2 + 8x) + (y^2 -  6y) = 11

Step 3: (x^2 + 8x + 16) + (y^2 - 6y + 9) = 11 + (16 + 9)

Step 4: (x^2 + 8x + 16) + (y^2 - 6y + 9) = 36

We factor out each quadratic

(x^2 + 8x + 16) = (x+4)(x+4) = (x+4)^2

((y^2 - 6y + 9)) = (x-3)(x-3) = (x-3)^2

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You can find some reference below:

https://math.wvu.edu/~hlai2/Teaching/Tip-Pdf/Tip1-29.pdf
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