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3 years ago

14

Tom created a mixed-media mural of a flag to celebrate the 4th of July. He spent $57 on paint and 4 times as much on fabric. How

many money did he spend altogether?

1 answer:

ki77a [65]3 years ago

4 0

Answer:

$285

Step-by-step explanation:

57 by 4 is 228 then add 57 to 228 which is 285

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Let f(x) = 5x – 8 and g(x) = 9 - 6x2.<br> -<br> (f o g)(-3) =

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Step-by-step explanation:

f(x) = 5x - 8

g(x) = 9 - 6x²

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2 years ago

Use the formula for the cosine of the difference of two angles to find the exact value of the following expression.

Zolol [24]

Answer:

Exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

Step-by-step explanation:

Given:

Cos(45° - 60°)

We have to apply the formula of cosine for difference of the two angles.

Formula:

$cos(a-b)=cos(a)\ cos(b)+sin(a)\ sin(b)$

Plugging the values.

⇒ $cos(45-60)=cos(45)\ cos(60) + sin(45)\ sin(60)$

We know that the values :

$sin(45) =cos(45) = \frac{1}{\sqrt{2} }$

$sin(60)=\frac{\sqrt{3} }{2}$ and $cos(60)=\frac{1}{2}$

So,

⇒ $cos(45-60)=(\frac{1}{\sqrt{2} } \times \frac{1}{2} ) + (\frac{1}{\sqrt{2} } \times \frac{\sqrt{3} }{2})$

⇒ $cos(45-60)=(\frac{1}{2\sqrt{2} } + \frac{\sqrt{3} }{2\sqrt{2} })$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )$

⇒ $cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )\times \frac{2\sqrt{2} }{2\sqrt{2} }$ ...<em>rationalizing </em>

⇒ $cos(45-60)=\frac{2\sqrt{2} +2\sqrt{6} }{ 8}$

⇒ $cos(45-60)=\frac{2(\sqrt{2}+\sqrt{6})}{8}$ ...<em>taking 2 as a common factor</em>

<em>⇒ </em> $cos(45-60)=\frac{(\sqrt{2}+\sqrt{6})}{4}$

To find the exact values we have to put the values of sq-rt .

As<em>, </em> $\sqrt{2}=1.41$ and $\sqrt{6} =2.44$

Then

<em>⇒ </em> $cos(45-60)=\frac{( 1.41+2.44)}{4}$ <em />

<em>⇒ </em> $cos(45-60)=\frac{( 3.85)}{4}$ <em />

⇒ $cos(45-60)=0.96$

So the exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

3 0

3 years ago