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PilotLPTM [1.2K]
3 years ago
9

Please identify the common angles and sides or if there are non. Explain all work please!

Mathematics
1 answer:
vova2212 [387]3 years ago
8 0

Answers:

Common angles: ΔBGC and ΔGDC

Common sides: ΔGE and ΔAG

A common angle is a triangle that exists in two or both of the triangles.

Here, the common angles should be ΔBGC and ΔGDC.

These two angles are triangles, and they consist in both triangles.

A common side is when two angles have one vertex in the same area.

Here, we see that the common sides are ΔGE, because they intersect.

Another common side we see here is ΔAG, because they also intersect.

Hope this answer helps you!

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Explain how to find each root, with its multiplicity, for the polynomial y=x^5-27x^2.
Nuetrik [128]

The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

The characteristics of the polynomial can be derived from algebraic techniques. Roots and multiplicity can be found by <em>factoring</em> the polynomial. The multiplicity is represented by a power binomial of the form:

(x-r_{i})^{m},\,m \le n (1)

Where n is the grade of the polynomial.

Now we proceed to factor the formula:

y = x^{5}-27\cdot x^{2}

y = x^{2}\cdot (x^{3}-27)

y = x^{2}\cdot (x^{2}+3\cdot x +9)\cdot (x-3)

Please notice that x^{2}+3\cdot x + 9 have two complex roots.

y = x^{2}\cdot \left(x+\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}  \right)\cdot \left(x+\frac{3}{2}+i\,\frac{3\sqrt{3}}{3}  \right)\cdot (x-3)

The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

We kindly invite to see this question on polynomials: brainly.com/question/1218505

7 0
3 years ago
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