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taurus [48]
1 year ago
15

Gcf of -15xyz, -55xy²,- 55yz

Mathematics
1 answer:
GalinKa [24]1 year ago
3 0

Answer:

-5y

Step-by-step explanation:

15 = 3×5

55 = 5×11

-15xyz = -1 × 3 × 5 × x × y × z

-55xy² = -1 × 5 × 11 × x × y²

-55yz = -1 × 5 × 11 × y × z

HCF = multiply all common factors with the lowest power amongst all 3 expressions

HCF = -1 × 5 × y = -5y

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2 years ago
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9514 1404 393

Answer:

  a) x = (√5 -1)/2 ≈ 0.618034

  b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

<u>Given</u>:

  x/(1 -x) = 1/x

<u>Find</u>:

  Exactly, and as a decimal approximation, ...

  a) x, using the quadratic formula

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The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

  x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}

We are only interested in the positive solution, which is ...

  \boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}

__

b) The quadratic we developed in the first part can be rearranged like this:

  x² +x = 1 . . . . . . add 1 to both sides

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  \dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}

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