Given the regular hexagon, find the measure of each numbered angle.
2 answers:
Answer:
m∠1=60°, m∠2=30°, m∠3=60°
Option C is correct.
Step-by-step explanation:
Given a regular hexagon
we have to find the measure of ∠1, ∠2 and ∠3
As the angle formed at the centre of circle is 360° and the diagonals of hexagon divides the hexagon into 6 congruent triangles implies the angle at the centre of these 6 congruent triangles are equal.
∴
In ΔFOE, by angle sum property
∠FOE+∠OEF+∠3=180°
60°+2∠3=180° (∵ OF=OE both are radius)
2∠3=120°
∠3=60°
⇒ ΔFOE is equilateral triangle.
Hence, all 6 are equilateral triangles
In ΔOGD, by angle sum property
∠2+∠OGD+∠ODG=180°
∠2+90°+60°=180
∠2=30°
∠1=60°, ∠2=30°, ∠3=60°
Hence, option C is correct.
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Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
__
<h3>Step 1</h3>Write the equation in standard form.
4x³ -16x² -84x = 0
<h3>Step 2</h3>Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
<h3>Step 3</h3>Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
<h3>Step 4</h3>Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
<h3>Step 5</h3>Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
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<em>Additional comment</em>
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
