An object is dropped off a cliff and falls freely. it speeds up as it falls toward the ground. the graph below shows the velocity in meters per second (m/s) of the object (denoted by the vertical axis) as a function of time in seconds (denoted by the horizontal axis). note that the relationship is linear. this relationship is given by the equation, v = gt. in this equation, g is the acceleration due to gravity, t is the number of seconds, and v is the velocity of the falling object. note that g is a constant. find and interpret the meaning of the initial value and the rate of change in this context. the initial value is 9.8. that means that object’s initial velocity 9.8 m/s. the rate of change is 9.8. that means the acceleration due to gravity is 9.8 m/s2. the initial value is 0. that means that object’s initial velocity 0 m/s. the rate of change is 98. that means the acceleration due to gravity is 98.0 m/s2. the initial value is 0. that means that object’s initial velocity 0 m/s. the rate of change is 9.8. that means the acceleration due to gravity is 9.8 m/s2. the initial value is 9.8. that means that object’s initial velocity 9.8 m/s. the rate of change is 0.98. that means the acceleration due to gravity is 0.98 m/s2.

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.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

asdsaddsa

step-by-step explanation:

i wish i could you, i have no idea how to answer this

step-by-step explanation: