Zipora wants to construct a triangle that has the following angle measures: 50°, 75°, and 55°. how many triangles can she make? none exactly one exactly three an infinite number

 an infinite number

Step-by-step explanation:

Given : Zipora wants to construct a triangle that has the following angle measures: 50°, 75°, and 55°.

The sum of the angles =  50°+75°+55°=180° = Sum of all angles of a triangle.

So a triangle is possible with this measurement.

But more than one triangle is possible of the given measurement because we have given only the measures of the interior angles but not the sides.

All triangles with the same angle measure would be similar to each other by the AAA-similarity criteria but with different proportional side-lengths.

[∵ Corresponding sides of similar triangles are proportional.]

Hence, She can make an infinite number of triangles.

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!

i hope this is what you were looking for.

see attached graph