The answer is C~1.83 carats. I hope I helped!
Well.....2.82 divided by 1 = 2.82
<h3>
Answer: angle B = 47 degrees</h3>
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Work Shown:
Use law of cosines to find angle B
b^2 = a^2 + c^2 - 2*a*c*cos(B)
9^2 = 6^2 + 12^2 - 2*6*12*cos(B)
81 = 36 + 144 - 144*cos(B)
81 = 180 - 144*cos(B)
81 - 180 = -144*cos(B)
-99 = -144*cos(B)
-144*cos(B) = -99
cos(B) = (-99)/(-144)
cos(B) = 0.6875
B = arccos(0.6875)
B = 46.5674634422102
B = 47 when rounding to the nearest whole number
Make sure your calculator is in degree mode.
arccos is the same as inverse cosine often labeled 
on calculators.
The answer is: " y − 1 = - 3(x + 2) " .
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Explanations:
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<u>Note</u>: The "point-slope form" of the equation of a line is:
→ " y − y₁ = m(x −x₁) " .
We are given the slope, m" , is: " - 3 " ;
We are given a point on the line [on the graph that is represented by this equation]; with the coordinates: " (-2 , 1) " ;
→ which is in the format: " (x₁ , y₁) " ;
→ As such: " x₁ = -2 " ; " y₁ = 1 " ;
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As aforementioned, the equation of a line in "point-slope form" ; is:
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→ " y − y₁ = m(x − x₁) " ;
in which:
→ "(x₁ , y₁) " represents the coordinates of a given point on the [line of the graph represented by the equation] ; AND:
→ " m " = the slope of the line [represented by the equation] " ;
We proceed by substituting our known values for "m" ; "y₁" ; and "x₁" :
→ " y − 1 = - 3(x − (-2) ) " ;
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→ Rewrite as:
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→ " y − 1 = - 3(x + 2) " ;
→ which is our answer; since it is written in "point-slope form" .
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