Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle.

x = 9.8

Step-by-step explanation:

(please refer to attached)

after labeling the picture with all the known information, we can see that

OF = OR = Radius of the circle     -----(eq 1)

Consider triangle OFP,  by Pythagorean theorem,

OF² = PF²+OP²

r² = 11.5² + 11²

r² = 253.25  -----(eq 2)

Consider triangle ORQ,  by Pythagorean theorem,

OR² = RQ²+OQ²

r² = 12.5² + x²

r² = 156.25 + x²  ----(eq 3)

equating (eq 2) and (eq 3)

253.25 = 156.25 + x²    

x² = 253.25 - 156.25

x² = 97

x = √97

x = 9.8  (nearest tenth)

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

equation image indicator

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

equation image indicator

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

equation image indicator

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!

idk i would have to be there to under stand it

step-by-step explanation:

idk i would have to be there to under stand it