6 Beers in a Six Pack?
6*abs(b - p) which can also be written as 6*|b - p|
The two numbers are 18 and -24.If you're having trouble with the factoring, you can always use the quadratic formula:Let the two numbers be a & b. a*b = P and a+b = S {for Product and Sum}So substitute b = S-a {from the Sum formula}, and you have a*(S-a) = P, or:a*S - a² = P ----> a² - S*a + P = 0.So with the quadratic formula:a1 = (-S + sqrt(S^2 - 4*1*P)/(2*1) Anda2 = (-S - sqrt(S^2 - 4*1*P)/(2*1)Substituting -432 for P and -6 for S, we get a1 = 18, and a2 = -24. Note that substituting a1 into the original formulas, gives b = a2, or if you use a2, then you get b=a1. So the two numbers are a1 and a2.
how to solve 7 + p = p +7
B
Given the graphic capability of this site, you are going to have to use some imagination! <---------a---------> <---a-b---><--b--> +-----------+-------+ |...............|..........| |.......P......|....Q...| |...............|..........| +-----------+-------+ |.......R......|....S....| |...............|..........| +-----------+-------+ In the above graphic, P, S and the whole figure are meant to be squares. The total area is P+Q+R+S = a2 P = (a-b)2 Q = b*(a-b) = (a-b)*b = a*b - b2 R = (a-b)*b = a*b = a*b - b2 and S = b2 Now, P = {P+Q+R+S} - Q - R - S = a2 - ab + b2 - ab + b2 - b2 = a2 - 2ab + b2
P. B. S. Pinchback died on 1921-12-21.
P. B. S. Pinchback was born on 1837-05-10.
S. P. B. Charan was born on 1974-01-07.
Solid and liquid.
Consider the three events: A = rolling 5, 6, 8 or 9. B = rolling 7 C = rolling any other number. Let P be the probability of these events in one roll of a pair of dice. Then P(A) = P(5) + P(6) + P(8) + P(9) = 18/36 = 1/2 P(B) = P(7) = 6/36 = 1/6 and P(C) = 1 - [P(A) + P(B)] = 1/3 Now P(A before B) = P(A or C followed by A before B) = P(A) + P(C)*P(A before B) = 1/2 + 1/3*P(A before B) That is, P(A before B) = 1/2 + 1/3*P(A before B) or 2/3*P(A before B) = 1/2 so that P(A before B) = 1/2*3/2 = 3/4
If a is rational then there exist integers p and q such that a = p/q where q>0. Similarly, b = r/s for some integers r and s (s>0) Then a*b = p/q * r/s = (p*r)/(q*s) Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0 Thus a*b can be expressed as x/y where p and r are integers implies that x = p*r is an integer q and s are positive integers implies that y = q*s is a positive integer. That is, a*b is rational.
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