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...

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...

the unit rate, in chapters per hour, would be how many chapters in one hour --- but, for 23 chapters/78 hours = this fraction (23/78) is already in simplified (i.e., reduced) form --- i.e., 23 is prime, and 78 = 2(39) = 2(3)13, so 23 and 78 contain no factors in common --- so, the unit rate would...

6x + 2y = what???

Word Problem Division Tricky (answer)

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 ...

Math help needed ASAP!!!! (answer)

log[x(x-9)] = log(x) + log(x - 9); use log(AB) = log(A) + log(B)

let x = number of horses in first stable now ---> x = y + 20 now ---> later, there will be x + 8 = y + 28 horses in stable 1 let y = number of horses in second stable now ---> later, there will be y + 2 horses in stable 2 thus, y +...

Word Problem with Equal Lengths (answer)

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)

Geometric Series: nth term = a(r^(n-1)) = 1536[(1/2)^(n-1)] = 24 ---> (1/2)^(n-1) = 24/1536 = 1/64 = 1/(2^6) = (1/2)^6 ---> n - 1 = 6 ---> n = 7 [24 is 7th term, with 1536 being the 1st term, and the common ratio being (1/2)]

area of circle of radius r is: A = (pi)(r^2), where pi = 3.14159.....; and r = d/2, where d = diameter of circle of 24 ---> r = 24/2 = 12 ---> A = (pi)(12^2) = 144(pi)

since foci are symetrically located on x-axis about origin, the equation of the ellipse must be of the following form: (x^2)/(a^2) - (y^2)/(b^2) = 1, where a = semi-major axis, and b = semi-minor axis, and: e = eccentricity = sqrt(a^2 - b^2)/a = 0...

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...

A*B*.0333+A=C solve for B (answer)

0.0333AB + A = C; 0.0333AB = C - A; B = (C - A)/(0.333A)

x = [(x1 + e1) + (x2 + e2) + (x3 + e3)]/3 = (x1 + x2 + x3)/3 + (e1 + e2 + e3)/3

f(x) = 4x - 3; g(x) = 3x + 2; g(f(4)) = g[4(4) - 3)] = g(16-3) = g(13) = 3(13) + 2 = 39 + 2 = 41

h(t) = -6(t - 2.5)^2 + 38.5; assume that h(t) is measured from ground level, in which case (incidentally) h(0) = -6(2.5^2) + 38.5 = 38.5 - 6(6.25) = 38.5 - 36 - 1.5 = 1; then, h(T) = 0, when ball hits ground; or, -6(T - 2.5)^2 +38...

f(x) = 4x - 3; g(x) = 3x + 2; g(f(x)) = g(f) = 3f + 2 = 3(4x - 3) + 2 = 12x - 12 + 2 = 12x - 10