Factor 12x2 23x 10 Simplify 4x1x4 3x1x1 2 Simplify 25i34

Factor: 12x^2 - 23x + 10 Simplify: 4x+1/x+4 + 3x-1/x+1 = 2 Simplify: 2-5i/3+4i Solve the absolute value equation: 2 + 2|2x + 5| = 26 Solve by any method: 4x^2 = 4x - 15 Find the equation of a line through the point (4, -2) And perpendicular to the line 3x - 2y = 4 Find the following composition of functions for f(x) = 6/x-2, g(x) = 3/5x: (f g)(x).(g f)(x) Simplify: 12x^1/6 y^1/4/16x^3/4 y^1/2 solve: squareroot -9x-9 + x = 1 Use the vertex formula to find the vertex for the function f(x) = -2x^2 - 6x - 1 Write the function in standard form.

Solution

1) correct

2) ( 4x+1)/(x+4) + (3x-1)/(x+1) = 2

take lcd as (x+4)(x+1)

[(4x+1)(x+1) + (3x-1)(x+4)]/(x+4)(x+1) =2

[ 4x^2 +5x +1 + 3x^2+11x -4 ]/(x^2 +5x +4) =2

7x^2 +16x -3 = 2x^2 + 10x +8

5x^2 +6x -11 =0

5x^2 +11x -5x -11 =0

x(5x+11) -1(5x +11) =0

(x-1)(5x +11) =0

x=1 ; x=-11/5

4) 2+ 2|2x +5| = 26

2 + 2(2x +5) =26

4x +10 +2 =26

4x = 26 -12

4x = 14

x= 7/2

2 - 2(2x +5) =26

2 - 4x -10 = 26

-4x = 34

x = -17/2

Solution ( -17/2 , 7/2)

5) 4x^2 = 4x -5

4x^2 -4x +5 =0

Solve using quadratic root formula:

x = ( -b +/- sqrt(b^2 -4ac) )/2a

= ( 4 +/- sqrt(16 -80))/8

= 1/2 +/- i

= 1/2 +i , 1/2 -i