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3 years ago

The license fee for a car which cost $7,000 is $77. At the same rate, what is the license fee for a car that cost $9,200?

Mathematics

1 answer:

Ymorist [56]3 years ago

4 0

The answer is 77*9200/700 = 101.2

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use compound angle formulae to find sin 15 and cos 15 in form of [ surd a (surd b + c) ] . Hence, find tan 15 in the simplest su

inysia [295]

Answer:

see explanation

Step-by-step explanation:

Using the difference formulae for sine and cosine

sin(x - y) = sinxcosy - cosxsiny

cos(x - y) = cosxcosy + sinxsiny

sin15° = sin(45 - 30)°

sin(45 - 30)°

= sin45°cos30° - cos45°sin30°

= $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ - $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$

= $\frac{\sqrt{6} }{4}$ - $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}-\sqrt{2} }{4}$

----------------------------------------------------------------------------------

cos15° = cos(45 - 30)°

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ + $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}+\sqrt{2} }{4}$

-------------------------------------------------------------------------------------

tan15° = $\frac{sin15}{cos15}$

= $\frac{\sqrt{6}-\sqrt{2} }{4}$ × $\frac{4}{\sqrt{6}+\sqrt{2} }$

= $\frac{\sqrt{6}-\sqrt{2} }{\sqrt{6}+\sqrt{2} }$

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator, that is ( $\sqrt{6}$ - $\sqrt{2}$ )

= $\frac{(\sqrt{6}-\sqrt{2})^2 }{(\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2}) }$

= $\frac{6-4\sqrt{3}+2 }{6-2}$

= $\frac{8-4\sqrt{3} }{4}$

= 2 - $\sqrt{3}$

5 0

2 years ago

84 + 45 = 3(28 + 15) Yes or No

Ronch [10]

yes

84+45= 129

28+15=43

43*3=129

3 0

2 years ago

1. If 8x + 4y = 44, what is the value of 6x + 3y?

rewona [7]

The value of the expression 6x+3y is 33

<h3>System of equations</h3>

System of equations consists of two or more equation with unknown variables.

Given the equation below

8x + 4y = 44,

Factor out 4 from the equation to have:

4(2x+y) = 44

Divide both sides by 4

2x+y = 11

Determine the value of 6x+3y

6x+3y = 3(2x+y)

6x+3y = 3(11)

6x+3y =33

Hence the value of the expression 6x+3y is 33

Learn more on equation and expression here: brainly.com/question/723406

#SPJ1

7 0

1 year ago

PLEASE HELP PICTURE SHOWN

jeka94

C
YOUR ANSWER IS C BECAUSE ITS EQULVILENT

7 0

2 years ago

What is 22/3 times 49/10

noname [10]

Answer:

22/3×49/10=35 14/15

Explanation:

$\frac{22}{3}$ × $\frac{49}{10}$ = $\frac{1078}{30}$

<em>Simplify:</em>

$\frac{1078}{30}$ ÷2= $\frac{539}{15}$

<em>Turn it into a mixed number:</em>

539÷15=35 <em>r</em>14

3 0

3 years ago