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Expansion of the given expression will result in x to the 3rd power, as there are 3 parts involving x, multiplied together. Let's ignore -5x for a second, and multiply the two expressions in brackets (usi...

Take the number that is in the root sign, and change it to 2 numbers multiplied together (we want one of these numbers to be a square number). A square number is 1, 4, 9, 16 etc. Then separate this into t...

this formula is used in triangles to define either a cosine or the side of the triangle opposite of the cosine's angle

c²=a²+b²-2abcosc

cosc= the cosine of t...

Gradient of initial line = 3/4 Equation of initial line : y= 3/4x + 5/4 (4y = 3x + 5) Equation of perpendicular line : y= -4/3x 

a.) simplify and expand (x+3)(2x+5) Expand using "crab claw" (better known as foil) => 2x^2 + 5x + 6x + 15 Simplify => 2x^2 +11x + 15 b.) differentiate (x+3)(2x+5) Using part a,  dy/dx= 4x...