Answer:
∠CBD = 125°
Step-by-step explanation:
The angle sum theorem tells you that ...
∠ABC +∠CBD = ∠ABD
8x -41° +9x +17° = 180° . . . . . . a "straight angle" has a measure of 180°
17x -24° = 180° . . . simpify
17x = 204° . . . . . . add 24°
x = 12° . . . . . . . . . . divide by 17
Now the measures of the angles can be found from their expressions.
∠ABC = 8(12) -41° = 55°
∠CBD = 9(12) +17° = 125°
Answer:
176
Step-by-step explanation:
91/9.10=0.10
17.60/0.10=176
Answer:

Step-by-step explanation:
We want to find the minimum-degree polynomial with real coefficients and zeros at:

As well as a <em>y-</em>intercept of 64.
By the Complex Root Theorem, if <em>a</em> + <em>b</em>i is a root, then <em>a</em> - <em>b</em>i is also a root.
So, a third root will be 4 - 4i.
The factored form of a polynomial is given by:

Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros. More factors can be added if necessary.
Substitute:

Since we want the minimum degree, we won't need to add any exponents.
Expand the second and third factors:

Hence:

Lastly, we need to determine <em>a</em>. Since the <em>y-</em>intercept is <em>y</em> = 64, this means that when <em>x</em> = 0, <em>y</em> = 64. Thus:

Solve for <em>a: </em>

Our factored polynomial is:

Finally, expand:

<span>c.
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Answer:
Sin (E) = √74/(2√23)
Step-by-step explanation:
Reference Angle = E
Hypotenuse = 2√23
Adjacent = 3√2
Opposite = DC = √(2√23)² - (3√2)²) = √(4*23 - 9*2) = √(92 - 18) = √74 (pythagorean theorem)
Recall SOHCAHTOA.
Thus,
Sin (E) = opp/hyp
Sin (E) = √74/(2√23)