Mathematics, 14.07.2019 09:30 jetblackcap

Triangle mno is equilateral. find x and y. (i've been stuck on this problem for the longest time, and i need ! picture below.)

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Again, your getting lost in the numbers. just think simply. a triangle has 180° and equilateral means all angles are exactly the same. Because of this, you know that m,n&o all equal 60°.

now it gets a little more complex when you split that to the smaller triangle and each of those have 180° within them.

it's safe to say that N is splitting it's full 60° equally between the three within it. making each one of the points at N equal to 20°. so solve for the rest to get y°.

We know M= 60°, O= 60°, N= 60° (20°,20°,20°) so to complete the triangle on the left we have one more angle that must be 100°. to complete the triangle on the right we have one more angle that must be 100° and to complete the center triangle we only know of 20° but have two equal angles left. So 180°-20°=160°. 160°÷2angles= 80° per angle to complete the center triangle.

that gives us y°=80°.

the X's are adding the smaller triangles to make the bigger triangle. so take 2x+4x+2x and divide that from the big triangle 180°. 8x=180° means x°=22.5°

Answer from: Quest

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

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