In the diagram below, ABCD is a rectangle.

9514 1404 393

  BC = 10 ft

Step-by-step explanation:

You may recognize the ratio of the given leg and hypotenuse of triangle BCD is 24 : 26 = 12 : 13. You may recall that the Pythagorean triple (5, 12, 13) is commonly seen in math problems. Here, that means side BC is 2×5 = 10 feet.

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If you don't recall these helps, you can use the Pythagorean theorem to find BC.

  BC² + DC² = DB²

  BC² = DB² -DC² = (26 ft)² -(24 ft)² = 676 ft² -576 ft² = 100 ft²

  BC = √(100 ft²) = 10 ft

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!

8 apples are left.

step-by-step explanation:

10-2=8

10 apples

take 2

now u have 8