In expanded form, 4.56 x 10-9 is 0.00000000456 .
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This is an algebra problem. There will be 2 equations and 2 unknowns. Let x = amount of 7% solution, and y = amount of 19% solution. .07x + .19y = .15*456. x + y = 456; or x = 456-y which will substitute into the first equation. .07(456-y) +.19y = .15*456. 31.92-.07y+.19y = 68.4. .12y = 36.48. y = 304L (amount of 19% solution to add). x = 456-y. x = 456 - 304. x = 152L (amount of 7% solution to add).
4.414*109 = 4,414,000,000
x + y = -7xy = -15y = -x - 7x(-x - 7) = -15-x^2 - 7x = -15 multiplying both sides by -1x^2 + 7x = 15 complete the square;(x^2 + 7x + 49/4) = 15 + 49/4(x + 7/2)^2 = 109/4(x + 7/2) = (plus & minus)square root of 109/41. x = -7/2 + (square root of 109)/22. x = -7/2 - (square root of 109)/2y = -x - 7y = -[-7/2 + (square root of 109)/2] - 7 = 7/2 - (square root of 109)/2 - 71. y = -7/2 - (square root of 109)/2 ory = -x - 7y = -[-7/2 - (square root of 109)/2] - 7 = 7/2 + (square root of 109)/2 - 72. y = -7/2 + (square root of 109)/2 Check it:
Use the formula I = P x R x TWhere I=interestP=principal investmentR=interest rateT=time in yearsIn this case, we want to know R, so re-arrange the formula to get:R = I / (P x T)=456/ (1600x6)=456/9600=0.0475=4.75%
In order to add or subtract numbers with exponents, the exponents must be the same. In order to multiply numbers with exponents, you complete the multiplication and add the exponents. In order to divide numbers with exponents, you complete the division, and subtract the bottom exponent from the top exponent. Examples: Addition: 4.6 x 107 + 2.5 x 109 = 0.046 x 109 + 2.5 x 109 = 2.546 x 109 Subtraction: 6.7 x 108 - 2.1 x 105 = 6.7 x 108 - 0.0021 x 108 = 6.66979 x 108 Multiplication: 5.3 x 102 x 8.4 x 106 = 44.52 x 102+6 = 44.52 x 108 = 4.452 x 109 Division: 6.2 x 1012/3.1 x 106 = 2.0 x 1012-6 = 2.0 x 106