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3 years ago

Use the substitution method to solve the system of equations. choose the correct ordered pair. 2x - y = 103x - 2y = 8

1 answer:

8 0

$2x-y=10\Rightarrow 2x-10=y \\ 
\Longrightarrow 3x-2y=8\Rightarrow 3x-2(2x-10)=8 \\ 
3x-4x+20=8 \\ -x=8-20=-12 \\ x=12 \\ \\ y=2(12)-10=24-10 \\ y=14 \\ \\ (x,y)=(12,14)$

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Consider the following division of polynomials.

Bond [772]

$x^4=x^2\cdot x^2$ . Multiplying the denominator by $x^2$ gives

$x^2(x^2+2x+8)=x^4+2x^3+8x^2$

Subtracting this from the numerator gives a remainder of

$(x^4+x^3+7x^2-6x+8)-(x^4+2x^3+8x^2)=-x^3-x^2-6x+8$

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This last remainder is exactly the same as the denominator, so $x^2+2x+8$ divides through it exactly and leaves us with 1.

What we showed here is that

$\dfrac{x^4+x^3+7x^2-6x+8}{x^2+2x+8}=x^2-\dfrac{x^3+x^2+6x-8}{x^2+2x+8}$

$=x^2-x+\dfrac{x^2+2x+8}{x^2+2x+8}$

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and this last expression is the quotient.

To verify this solution, we can simply multiply this by the original denominator:

$(x^2+2x+8)(x^2-x+1)=x^2(x^2-x+1)+2x(x^2-x+1)+8(x^2-x+1)$

$=(x^4-x^3+x^2)+(2x^3-2x^2+2x)+(8x^2-8x+8)$

$=x^4+x^3+7x^2-6x+8$

which matches the original numerator.

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Marat540 [252]

D. 1/4 (-x+2)

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3 years ago

A rectangle garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet

Lana71 [14]

Width = 4ft

Length = 6ft

<u>Explanation: </u>

Let length = l ,

So, width = 2l-8

Perimeter of rectangle = 2x(length + width)

According to the question,

$20ft = 2X(l + 2l-8)\\20ft = 2X(3l -8)\\ 10ft = 3l-8\\18ft = 3l \\ l = 6ft$

Hence,

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