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First six triangula numbers?
1 (0+1) 3 (0+1+2) 6 (0+1+2+3) 10 (0+1+2+3+4) 15 (0+1+2+3+4+5) 21 (0+1+2+3+4+5+6) Notice these are the numbers you can arrange into equalateral triangles.
What is the slope of the given points (0-1) and (-2-4)?
Points: (0, -1) and (-2, -4)Slope: 3/2
What is the range of 0 1 2 3 4 5 6?
The range of {0, 1, 2, 3, 4, 5, 6} is 6 - 0 = 6.
What is the standard deviation of 1 2 3 4 5 6 7 8 9?
2.738612788 First, find the mean (average) of all the numbers: 1+2+3+4+5+6+7+8+9 = 45 45 / 9 = 5 Mean is 5 Now take every number and calculate how far it is away from the mean, then square that number 1-5 = -4 ^2 = 16 2-5 = -3 ^2 = 9 3-5 = -2 ^2 = 4 4-5 = -1 ^2 = 1 5-5 = 0 ^2 = 0 6-5 = 1 ^2 = 1 7-5 = 2 ^2 = 4 8-5 = 3 ^2 = 9 9-5 = 4 ^2 = 16 Next, add all the results: 16+9+4+1+0+1+4+9+16 = 60 Then divide by the sample size minus 1 (n-1): 60 / 8 = 7.5 Finally, find the square root of that number: 7.5^ 0.5 = 2.738612788 Answer: 2.738612788
How do you factor x squared plus x minus one half?
(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
