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3 years ago

X is an integer Write down all the solutions of inequality 3<2x +1 < 13

Mathematics

1 answer:

BaLLatris [955]3 years ago

6 0

Answer:

1<x<6

Step-by-step explanation:

subtract 1 from every side: 2<2x<12

divide 2 every side: 1<x<6

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There was a bowl with 120 candies in it. Billy, Bob and Buck found the bowl. Billy ate 2/12 of the candies, Bob ate 3/12 and Buc

blagie [28]

Answer:

20 candies left.

Step-by-step explanation:

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3 years ago

Look at the picture below for the question i need help with. I pretty sure you need to find the y-intercept...

daser333 [38]

Answer:

20.00

Explanation:

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3 years ago

Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

MA_775_DIABLO [31]

Answer:

The answer is X=10

Step-by-step explanation:

3x10 = 30

30+6 = 36

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All exterior angle add up to 360 degrees.

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3 years ago

Express the complex number in trigonometric form -6 + 6sqrt3i

marusya05 [52]

$\large\begin{array}{l}\\\\ \textsf{This is a complex number in }\mathsf{a+bi}\textsf{ form:}\\\\ \mathsf{z=-6+6\sqrt{3}\,i}\\\\ \textsf{where }\mathsf{a=-6~~and~~b=6\sqrt{3}.} \end{array}$

$\large\begin{array}{l}\\\\ \bullet~~\textsf{1}\mathsf{^{st}}\textsf{ step: Find the absolute value of z (complex modulus of z):}\\\\ \mathsf{|z|=\sqrt{a^2+b^2}}\\\\ \mathsf{|z|=\sqrt{(-6)^2+(6\sqrt{3})^2}}\\\\ \mathsf{|z|=\sqrt{36+36\cdot 3}}\\\\ \mathsf{|z|=\sqrt{36\cdot 108}}\\\\ \mathsf{|z|=\sqrt{144}}\\\\ \mathsf{|z|=12} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{2}\mathsf{^{nd}}\textsf{ step: Find the argument }\mathsf{\theta}\textsf{ of z:}\\\\ \mathsf{arg(z)=\theta}\\\\ \textsf{is an angle that satisfies the following conditions:}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{a}{|z|}=\dfrac{a}{\sqrt{a^2+b^2}}}\\\\ \mathsf{sin\,\theta=\dfrac{b}{|z|}=\dfrac{b}{\sqrt{a^2+b^2}}} \end{cases}\qquad\quad-\pi$

$\large\begin{array}{l}\textsf{For }\mathsf{z=-6+6\sqrt{3}\,i,}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{-6}{12}=-\,\dfrac{1}{2}}\\\\ \mathsf{sin\,\theta=\dfrac{6\sqrt{3}}{12}=\dfrac{\sqrt{3}}{2}} \end{cases}\\\\\\ \textsf{Since}\\\\ \mathsf{cos\,\theta0,}\\\\ \theta\textsf{ lies in the 2}\mathsf{^{nd}}\textsf{ quadrant.}\\\\\\\textsf{Therefore,}\\\\ \mathsf{\theta=\dfrac{2\pi}{3}~rad~~(120^\circ)} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{3}\mathsf{^{rd}}\textsf{ step: Express z in the trigonometric form:}\\\\ \begin{array}{rcl} \mathsf{z}&\!\!=\!\!&\mathsf{|z|\cdot (cos\,\theta+i\,sin\,\theta)}\\\\ \mathsf{-6+6\sqrt{3}\,i}&\!\!=\!\!&\mathsf{12\cdot \left(cos\, \dfrac{2\pi}{3}+i\,sin\,\dfrac{2\pi}{3}\right)\qquad\quad\checkmark} \end{array} \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154167

$\large\textsf{I hope it helps.}$

Tags: <em>complex number trigonometric form trig absolute value modulus argument angle</em>

4 0

3 years ago

Javier is buying food in the lunch line . The tray of salad plates is 3/8 full . The tray of fruit plates is 3/4 full . Which tr

Marina CMI [18]

.. Please... Please tell me you know fractions at least well enough to know this ;_;

3/4 is like 0.75, yeh?
3/8 is like.. 0.365

Change the Denominator (Bottom Number in Fraction) so they're the same:
6/8 3/8.

Now d'you see?

5 0

3 years ago

Read 2 more answers