Key to the Practice Final

Problem 1

15x + 5 - 6x² - 2x - (16 - 2(4)(2x) + 4x² )

= 15x + 5 - 6x² - 2x - 16 + 16x - 4x²

= -10x² + 29x - 11

Problem 2

-8 < -4x < 4

2 > x > -1

Problem 3

A function is a rule that assigns to every element of a set (called the domain) to a unique element of a set (called the range)

Problem 4

2x²  + 7x + 21 + 59/(x - 3)

Problem 5

A.  2(x² - x) - (2x + 1) = 2x² - 2x - 2x - 1 = 2x² - 4x - 1

B.  (x² - x)(2x + 1) = 2x³ + x² - 2x²  - x = 2x³ - x²  - x

C.  Not covered in this class

D.  [((x + h)²  - (x + h)) - (x² - x)]/h = [x²  + 2xh + h²  - x - h - x² + x]/h

= (h² + 2xh - h)/h = h²/h + 2xh/h - h/h = h + 2x - 1

Problem 6

Problem 7

A.  y = 1/2x - 7/2,  y-int = -7/2, x-int = 7

B.  y = 3x - 1, y-int = -1, x-int = 1/3

Problem 8

Let x be the length of the shortest side

x + 50 is the length of the medium side

2x is the length of the longest side

then 450 < x + x + 50 + 2x < 490

450 < 4x + 50  < 490

400 < 4x  < 440

100 < x  <  110

Hence the shortest side needs to be between 100 feet and 110 feet.

Problem 9

[(-3x)^-3y⁶]/[2³(x³y^-1)^-6] = [y⁶(x³y^-1)⁶] /[(-3)³x³2³]

= y⁶x¹⁸y^-6/-27x³8 = x¹⁸/-216x³ = -x¹⁵/216 

Problem 10

1.1x10¹⁰ bits

Problem 11

A.  {x| x not -2/3}

B.  {x|x < 2}

Problem 12