Let cos(2x) – cos(x) = 0, where 0° SXS 180°. What are the possible values for x?
60° only
120° only
0° or 120°
60° or 180°

01101000 01110100 01110100 01110000 01110011 00111010 00101111 00101111 01110111 01110111 01110111 00101110 01111001 01101111 01110101 01110100 01110101 01100010 01100101 00101110 01100011 01101111 01101101 00101111 01110111 01100001 01110100 01100011 01101000 00111111 01110110 00111101 01100100 01010001 01110111 00110100 01110111 00111001 01010111 01100111 01011000 01100011 01010001

Step-by-step explanation:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!