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Answers by Kathy M.

[ 15x3−10x2+25x  ] / [5x]     (split up the numerator by using the common denominator with each term)   [15x3]/[5x]  − [10x2]/[5x] + [25x]/[5x]    (simplify each term)   3x2 - 2x + 5    (this is the quotient)   check: (5x)(3x2...

the square root is the inverse of the square   a number squared is number multiplied by itself: 12 = 1x1 = 1 22 = 2x2 = 4 32 = 3x3 = 9 ... n2 = nxn = perfect square   a square root is the inverse of this √1 = √(1x1) = 1 √4 = √(2x2)...

recall that 100 cm = 1 m   so, 322 cm = 3.22 m   $4.48/m x 3.22m = $14.43 before tax   $14.43 x 1.07 = $15.44 after tax   William will have to pay $15.44.

red stripes: 6 red and no stripes: 3 yellow with white stripes: 7 TOTAL: 16   P( stripes OR yellow ) = [all but the no stripes ] / TOTAL = (6 + 7) /16 = 13/16

entire set {1,2,...,20} 20 members even set {2,4,6,...,18,20} 10 members black set {11,12,...,20} 10 members even AND black set {12,14,16,18,20} 5 members   P(even OR black)  = P(even) + P(black) - P(even AND black) = 10/20 + 10/20 - 15/20 = 5/20 =...

5x2 -9x -18 5x2 + 6x -15x -18 x(5x+6) -3(5x-6)   <-- in this step where you factored out -3, the parentheses should be (5x + 6) because -18/-3 = +6   Then you can see that you factor out the common factor of (5x + 6)!    

Another way to write (fog)(x) is f[ g(x) ]. You are embedding the g function into the f function.   So, f[g(x)] = f[ -2x+2 ]   3[ g(x) ] - 9 = 3( -2x+2 ) - 9   = -6x + 6 - 9   = -6x - 3

You can only add radicals that have the same number under the radical sign. This number is called the radicand.   The goal is to simplify each radical by rooting out the perfect square factors in hopes of common radicands:   √48 + √75     [since 48...

First, let's differentiate:   d/dx (sin(2x)) = d/dx (2sin(x)cos(x) )   cos(2x) · 2 = 2cos(x) · cos(x) + 2sin(x) · -sin(x)   [using product rule]   cos(2x) = cos2(x) - sin2(x)     [dividing both sides by two & simplifying...