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Word of the Day
invariable
Definition: (adjective) not changing or subject to change.
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Math Teaser
Problem
A group of 9 friends invest equally in a business opportunity that costs $20,000. If n more friends were to take part evenly in the investment...
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SAT* Tip of the Day
So What?
Math questions involving two equations and two unknowns can usually be combined into one equation with one unknown.
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PSAT: Math Question #5

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Question: What is the value of x in the figure below?



Choices:
A. 2
B. 3
C. 1
D. 2
E. 2 2

The correct answer is (D).

The correct answer is (D).
 Did you recognize the triangle as a  45  °   -  45  °   -  90  °   triangle, 
  which has sides in the ratio of 1:1: 
√
2
 ? If you did, you could  
 use that ratio to determine what  x  is. 
  
 First you want to determine a multiplier to use to convert our  
 1:1: 
√
2
 triangle to our example triangle - in other words, what 
 must you multiply 1 by to get 
√
2
 ? The answer is  
√
2
  
 So for x, we can multiply 
√
2
 from our standard   45  °  45  °  90  ° 
 triangle, by our multiplier: 
√
2

√
2
 × 
√
2
 =  2
a2  +  b2  =  c2
√
2
 squared   + 
√
2
 squared   =  c2
2  +  2  =  c2
4  =  c2
2  =  c

You can also solve this using the Pythagorean Theorem since it is has a 90 degree angle.The correct answer is 2.
  
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