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Salsk061 [2.6K]
3 years ago
10

An Inscribed angle with a diameter as a side has measure x degrees ? If the ratio of m overline AD to mDB is 1:4, what is mDB? (

Round to the nearest tenth If necessary).
Mathematics
1 answer:
Neko [114]3 years ago
8 0

Answer:

144

Step-by-step explanation:

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frutty [35]

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Step-by-step explanation:

This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.

  1. The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
  2. Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".

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2x^4+5x^3+5x^2+20x-12=(x^2+4)(2x^2+5x-3)

I'll go through to steps to factor that second expression below:

2x^2+5x-3=2x^2+6x-x-3\\=2x(x+3)-(x+3)\\=(2x-1)(x+3)

Solving both of the expressions when f(x) = 0 gets us our final two zeroes:

2x-1=0\\2x=1\\x=1/2

x+3=0\\x=-3

So, the remaining zeroes are 1/2 and 3.

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