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3 years ago

If f(x) = 6x2 - 4 and g(x) = 2x + 2, find (f - g)(x).

Mathematics

2 answers:

Hunter-Best [27]3 years ago

8 0

6x^2-2x-6 is the correct answer

Dafna11 [192]3 years ago

7 0

Answer:

6x² - 2x - 6

Step-by-step explanation:

note (f - g)(x) = f(x) - g(x), thus

f(x) - g(x)

= 6x² - 4 - (2x + 2) ← distribute

= 6x² - 4 - 2x - 2 ← collect like terms

= 6x² - 2x - 6

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Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°

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Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
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c=hypotenuse\\
a=adjacent\\
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\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
\\\\
-------------------------------\\\\
sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13} \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}$

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