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Sophie [7]
3 years ago
14

The figure shows a line graph and two shaded triangles that are similar:

Mathematics
1 answer:
dlinn [17]3 years ago
8 0

True:

3rd One

4th One

False: All of the others.

It's a straight line, so it is going to have straight qualities and straight inequalities throughout the graph.

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Solve for x.
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Answer:

x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}

Step-by-step explanation:

-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}

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The sequence a1, a2, a3, . . . , an of n integers is such that ak = k if k is odd and ak = –ak – 1 if k is even. Is the sum of t
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We will use the sine and cosine of the sum of two angles, the sine and consine of \frac{\pi}{2}, and the relation of the tangent with the sine and cosine:

\sin (\alpha+\beta)=\sin \alpha\cdot\cos\beta + \cos\alpha\cdot\sin\beta

\cos(\alpha+\beta)=\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta

\sin\dfrac{\pi}{2}=1,\ \cos\dfrac{\pi}{2}=0

\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha}

If you use those identities, for \alpha=x,\ \beta=\dfrac{\pi}{2}, you get:

\sin\left(x+\dfrac{\pi}{2}\right) = \sin x\cdot\cos\dfrac{\pi}{2} + \cos x\cdot\sin\dfrac{\pi}{2} = \sin x\cdot0 + \cos x \cdot 1 = \cos x

\cos\left(x+\dfrac{\pi}{2}\right) = \cos x \cdot \cos\dfrac{\pi}{2} - \sin x\cdot\sin\dfrac{\pi}{2} = \cos x \cdot 0 - \sin x \cdot 1 = -\sin x

Hence:

\tan \left(x+\dfrac{\pi}{2}\right) = \dfrac{\sin\left(x+\dfrac{\pi}{2}\right)}{\cos\left(x+\dfrac{\pi}{2}\right)} = \dfrac{\cos x}{-\sin x} = -\cot x
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