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Answers by Herb K.

1a-15=4a-3 (answer)

you subtract 4a from each side so as get both "a" terms on the left side, so that they can then be combined:     a - 15 = 4a - 3 ---> a - 4a - 15 = -3;  or, -3a - 15 = -3;  then add 15 to each side ---> -3a = -3 + 15 = 15 - 3 = 12;    then...

(q)  if you start with the Quadratic Equation, ax^2 + bx  + c = 0, then write the following to complete the square (the       following is essentially the derivation of the Quadratic Formula):        (i)    subtract "c"...

(n)  if the x-intercepts are (a,0) and (b,0), where a < b, then from the symmetry properties of the parabola, the x-coordinate of the vertex (usually denoted as "h") would be given as h = (a + b)/2, and the y-coordinate of the vertex (usually denoted as "k") would...

if we let x = dividend;  Q = quotient;   and  R = remaninder,  then we have the following:     x = 117(Q - 3) + R and  x = 171Q + R;  equating the two expressions for x, we find: 171Q + R = 117(Q - 3) + R   or:   171Q...

f(x) = x^2 is a parabola, with vertex at (0,0), and is therefore an EVEN function [symmetric about y-axis; f(-x) = f(x)]   g(x) = 2(x^2) + 1 is also a parabola, with vertex at (0,1), and also an EVEN function                    ...

140 = 2(70) = 2(2)(35) =  2(2)(5)(7)= 14(10)   168 = 2(84) = 2(2)(42) = 2(2)(2)(21) = 2(2)(2)(3)(7) = 14(12)   210 = 3(70) = 3(7)(10) = 3(7)(2)(5) = 2(3)(5)(7) = 14(15)   then, gcf(140,168,210) = 14 = greatest possible length of each of the smaller pieces...

5(m-n)-m(m-n) (answer)

let x = m - n;  then, 5(m - n) - m(m - n) = 5x - mx = (5 - m)x = (5 - m)(m - n)

Word Problem (answer)

F(x) = -0.018x^2 + 1.656x + 4.4;   I'm assuming that the middle term, 1.656, should read 1.656x   this is the equation of a parabola, F(x) = Ax^2 + Bx + C, with A = -0.018, B = 1.656, C = 4.4, opening downward (since A < 0), with   F(0) = 4.4   the...