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AlexFokin [52]
3 years ago
8

Which value of b will make the expression x^2+bx+120 factorable?

Mathematics
2 answers:
fenix001 [56]3 years ago
7 0

Answer:  12 b

These are the possible sums of the factor pairs of 12 b is the sum of the factors used to multiply to get 12 for the C value. ( x + 1) xx (x + 12) = x^2 + 13 x + 12 ( x - 1) xx (x - 12) = x^2 + (-13) x + 12 (x + 2) xx (x + 6) = x^2 + 8x + 12 (x - 2) xx (x - 6) = x^2 + (-8)x + 1

Oduvanchick [21]3 years ago
4 0

Answer:

Step-by-step expla These are the possible sums of the factor pairs of 12 b is the sum of the factors used to multiply to get 12 for the C value. ( x + 1) xx (x + 12) = x^2 + 13 x + 12 ( x - 1) xx (x - 12) = x^2 + (-13) x + 12 (x + 2) xx (x + 6) = x^2 + 8x + 12 (x - 2) xx (x - 6) = x^2 + (-8)x + 1

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Explanation:

I'm assuming that segments AD and CD are tangents to the circle.

We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.

By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.

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Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.

Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.

We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.

---------------------------

Here's what we have so far for quadrilateral DAEC

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Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees

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Or a shortcut you can take is to realize that angles E and D are supplementary

E+D = 180

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This only works if AD and CD are tangents.

Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.

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