LifeTrace is a very successful social media and business consulting firm.
Several times each quarter, the company pays for each employee's one-
hour massage and a one-hour personal training session at a local gym,
depending on the day and the employee's preference. Each massage
costs $40, while each personal training session costs $30. However, the
company's total cost for providing these services cannot exceed
$6,550.00 per quarter.
The following inequality represents the amount of money that Life Trace
spends on massages and personal training sessions.
40x + 30y = $6550

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation:

b

step-by-step explanation:

multiply terms on numerator/ denominator by (x - 1)

= ← distribute numerator/ denominator

= ← simplify

=

= → b