The amount y of your friend's allowance if the amount she receives is $77 more than the amount x you receive.

Mathematics

1 answer:

sergeinik [125]3 years ago

8 0

The amount y is equals to x+77

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Let v1 =(-6,4) and v2=(-3,6) compute the following what i sthe angle between v1 and v2

Agata [3.3K]

$\bf ~~~~~~~~~~~~\textit{angle between two vectors }
\\\\
cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies 
\measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right)\\\\
-------------------------------$

$\bf \begin{cases}
v1=\ \textless \ -6,4\ \textgreater \ \\
v2=\ \textless \ -3,6\ \textgreater \ \\
------------\\
v1\cdot v2=(-6\cdot -3)+(4\cdot 6)\\
\qquad \qquad 42\\
||v1||=\sqrt{(-6)^2+4^2}\\
\qquad \sqrt{52}\\
||v2||=\sqrt{(-3)^2+6^2}\\
\qquad \sqrt{45}
\end{cases}\implies \measuredangle \theta =cos^{-1}\left( \cfrac{42}{\sqrt{52}\cdot \sqrt{45}} \right)
\\\\\\
\measuredangle \theta =cos^{-1}\left( \cfrac{42}{\sqrt{2340}} \right)\implies \measuredangle \theta \approx 29.74488129694^o$

8 0

3 years ago

Solve and find the integer of 4x^2-19x-5

Anarel [89]

(x-5)(4x+1)
4x^2 times -5 is -20 the factors of -20 are -1x20, 1x-20... but to make the -19x you would add together the 1 and -20 because 1-20 is -19.
This then splits off to factorise 4x^2-20x, making this side 4x(1x-5) carry the brackets over to make it 1(1x-5) joining the brackets together to make (4x+1)(x-5)