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kolezko [41]
3 years ago
10

You buy the same number of brushes, rollers, and paint cans. Write an expression in simplest form that represents the total amou

nt of money you spend for
painting supplies... Brush cost $3.99, Paint cost $21.79 and Paint roller cost $6.89
Mathematics
1 answer:
Soloha48 [4]3 years ago
3 0

If you buy ' N ' of each item, then you'll pay  3.99N  for brushes,
21.79N  for cans of paint, and  6.89N  for rollers.

The question assures us that you bought the same number of
each item.  So your total bill at the hardware store checkout is

                      3.99N + 21.79N + 6.89N

                 =  N (3.99 + 21.79 + 6.89)

                 =        32.67 N .
 

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HELP! Find the value of sin 0 if tan 0 = 4; 180 &lt; 0&lt; 270
BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

\large \boxed{sin \theta = tan \theta cos \theta} \\  \large \boxed{tan^{2}  \theta + 1 =  {sec}^{2} \theta}

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

\large{ {4}^{2}  + 1 =  {sec}^{2} \theta } \\  \large{16 + 1 =  {sec}^{2} \theta } \\  \large{ {sec}^{2}  \theta = 17}

As we know, sec²θ = 1/cos²θ.

\large \boxed{sec \theta =   \frac{1}{cos \theta} } \\  \large \boxed{ {sec}^{2}  \theta =  \frac{1}{ {cos}^{2}  \theta} }

And thus,

\large{  {cos}^{2}  \theta =  \frac{1}{17}}   \\ \large{cos \theta =  \frac{ \sqrt{1} }{ \sqrt{17} } } \\  \large{cos \theta =  \frac{1}{ \sqrt{17} }  \longrightarrow  \frac{ \sqrt{17} }{17} }

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

\large{cos \theta =   \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta =  -  \frac{ \sqrt{17} }{17}}

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

\large{sin \theta = 4 \times ( -  \frac{ \sqrt{17} }{17}) } \\  \large{sin \theta =  -  \frac{4 \sqrt{17} }{17} }

Answer

  • sinθ = -4sqrt(17)/17 or A choice.
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