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Answers by Michael F.

1/|×-4|<1/|×+7| multiply both sides by |×-4|×|×+7| to get   |×+7|<|×-4| which says that the points you are looking for are those whose distance from -7 is less than their distance from 4. The middle of that interval is the point -3/2. The points we want...

(m-n)2=m2-2mn+n2=140-2(49)=140-98=42 You only asked for m-n. The question title asks for more.

solve the system (answer)

y=-x+7 y=(x-3)2/2=(x2-6x+9)/2 So -x+7=(x2-6x+9)/2 or -2x+14=x2-6x+9 or 0=x2-4x-5 competing the square we have (x-2)2-9=0 or x-2=±3 or x=5, or x=-1 In which cases y=2 or y= 8 (5,2) and (-1,8) are the solutions

x and y are two numbers each greater than 3, the highest common factor of x and y is 3, the lowest common multiple of x and y is 36, find x and y xy = product of greatest common divisor and least common multiple=3×36=108 Since GCD is 3 we may write x=3a, y=3b since...

Whatever the coefficients, we may write this as Acosx+Bsinx and so as √(A2+B2)[(A/√(A2+B2))cosx+(B/√(A2+B2))sinx] Let now cosθ=A/√(A2+B2)  and sinθ=B/√(A2+B2) the full expression is now √(A2+B2)cos(x-θ) You really must clarify the coefficients...

x+2y-3z=-5 2x+5y+z=12 x-4y-3z=-11 subtract twice the first equation from the second subtract the first equation from the third   x+2y-3z=-5     y +7z=22    -6y     =-6 y=1 from third equation use...

2) Let x be quantity of 20% alcohol Let y be quantity of 60% alcohol x+y=80 .2x+.6y=.3(80)   x+y=80 2x+6y=240   x+y=80 x+3y=120   2y=40 y=20 x=60    

The number of ways of choosing one person from each group is 5C1×8C1×5C1×10C1×4C1× 6C1=48000 The number of ways of choosing six people from 38 people is 38C6=2760681 The probability in question is the ratio 48000/2760681

(5x^2)-(2x-3)^2 (answer)

5x2-(2x-3)2=5x2-(4x2-12x+9)=5x2-4x2+12x-9=x2+12x-9 That's as far as I can go without seeing the choices