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valina [46]
3 years ago
8

Find the slope of the graphed line.

Mathematics
1 answer:
spin [16.1K]3 years ago
7 0

Answer:

-6/3

Step-by-step explanation:

Move down 6 from the top point.

Then move right 3 to the bottom point.

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Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?
bagirrra123 [75]
\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\

\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus         \bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]
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A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings they each have.
mihalych1998 [28]

Answer:

1.5

Step-by-step explanation:

Attached to this answer is the diagram of the box plot described in the question, and the means from the plot are calculated thus;

Students;    no. of siblings

student 0     2

student 1      4

student 2     7

student 3     5

student 4     2

Total             20

Mean no. of siblings = (total number of siblings) ÷ (total number of students)

Note that number of students here are the once that had at least one sibling, others without siblings are not used in the calculation, hence 5 students (student-0 to student-4) make up total number of students, while the remaining 4 students (student-4 to student-9) are disregarded.

Therefore, mean = 20 ÷ 5 = 4 siblings.

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Harold bought 20 toys for his nieces and nephews. The least expensive toy cost $8.21, and the most expensive toy cost $13.79. Wh
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The logical answer would be d

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