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1. The diagonal length of a cube is diagonal2=length2 + width2 + height2
2. The sum of two sides in a triangle must be greater than the third one.
3. The distance in a plane is distance2=(X2 - X1)2 + (Y2 - Y1)2
4. The midpoint in a place between two points (X1 + X2/2, Y1 + Y2/2)
5. Vertical lines do not have slopes
6. Slope=y2 -y1/x2-x1
7. If two nonvertical lines are perpendicular, the product of their slopes is -1: rs=-1
8. An altitude divides an equilateral triangle into two 30-60-90 right triangles.
9. In a 30-60-90 right triangle the sides are x, x31/2, and 2x
10. The sum of the lengths of any two sides of a triangle is less than the length of the third side.
11. The difference between teh lengths of any two sides of a triangle is less than the length of the third side.
12. The area of an equilateral triangle is s231/2/4
13. If two triangles are similar, the common ratio of their corresponding sides is called the ratio of similitude.
14. If two triangles are similar, and if k is the ratio of similitude, then:
a. The ratio of all the linear measurements of the triangles is k and b. the ratio of the areas of the triangles is k2.
15. The sum of the measures of the n angles in a polygon with n sides is (n-2) X 1800
16. In any polygon, the sum of the measures of the exterior angles, taking one at each vertex, is 3600.
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if f(x) is a function and b is a positive number:
19. In a arithmetic sequence whose common difference is d, then an= a1 + (n-1)d
20. In a geometric sequence whose common ratio is r, then an = a1(r)n-1
1500/Z*%: 15=X/100*Z X=1500/Z*%
5986.6245: digit in the thousands is at the left of the decimal and the thousandths at the right.
After he paid 20% of 60%, he still had 80% in hand out of 60%. So 80% * 60% = 48%.