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frozen [14]
3 years ago
15

(07.05 LC) What is the value of x in the equation −x = 2 − 3x + 6? (5 points) A. 8 B.4 C. −4 D. −8

Mathematics
1 answer:
Paraphin [41]3 years ago
5 0

Answer: B (x = 4)

- x = 2 - 3x + 6  combine like terms

- x = -3x + 8      add 3x

2x = 8               divide by 2

x = 4

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\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx

Notice that x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1). Decompose the integrand into partial fractions:

\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}
=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}

Integrating term-by-term, you get

\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx
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2 years ago
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Q.2 - What is the value of y in the equation 3(4y - 12) = 0 ? Show your work.
Alex

Hey there!

3(4y - 12) = 0

3(4y) + 3(-12) = 0

12y - 36 = 0

Add 36 to both sides

12y - 36 + 36 = 0 + 36

Cancel out: -36 + 36 because it give you 0

Keep: 0 + 36 because it help solve for the equation

New equation: 12y = 0 + 36

Simplify it

12y = 36

DIVIDE 12 to both sides

12y/12 = 36/12

Cancel out: 12/12 because that give you 1

Keep: 36/12 because it give you the y-value (also known as your overall result)

New equation: y = 36/12

Simplify it

y = 3


Therefore, your answer should be:

y = 3


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

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1 year ago
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