On a reality TV show Last Man Standing, a package is thrown from a plane to the ocean below. The contestants must swim to the package to receive the "free pass" located inside the package. The path that the package follows can be modelled by the quadratic functino d(t)= -4.9t²+10t+1200, where d represents the distance, in metres, that the package travels and t is the time in seconds. How long will it take for the package to reach the water?

The length of a rectangle is 6 cm more than the width, and the area is at least 91cm2. What are the possible dimensions of the rectangle?

police estimate the speed a car has been travelling by using the length of the skid marks. A formula used for this purpose is v=-7+8.2square root d, d>0, where v is the speed in kilometres per hour, and d is the length of the skid marks, in metres. 

a: Solve formula for d

b: For a car braking from a speed of 90km/h, what are the length of the skid marks to the nearest metre.

c: What would be the speed of the car, to the nearest kilometre per hour that would have created 150 skid marks?

Adding, subtracting, multiplying, and dividing rational expressions are similar to performing the same operations on rational numbers. Using examples for each operation, how do you support this statement?

The sum of the reciprocals of two positive consecutive integers is 31/240. Describe  what each of the expressions represents in relation to this problem.

a: x

b: x+1

c: 1/x

d: 1/x+1

e: 1/x+1/x+1

d: solve the problem 

adding, subtracting, multiplying, and dividing rational expressions are similar to performing the same operations on rational numbers. Using examples for each operation, support this statement.

an incorrect definition of an absolute value is

A: |x|= x for x>0, 0 for x=0, -x for x<0

B: |x|= x for x > or equal 0, -x for x<0

C: |x|= x for x>0, -x for x< or equal 0

D: |x|= x for x>0, -x for x<0

a clothing store is holding a buy one, get one half off sale for tshirts, where the second tshirt purchased is half the original price.

a; let b be the cost to the store to buy the shirts, and let s be the original selling price. write an inequality relating the two variables such that the store profits more from a customer purchasing two T-shirts then from a customer purchasing one.(hint: the expression s-b represents the profit when one shirt is purchased. What is an expression for the profit when two shirts are purchased?)

b; isolate b in the inequality. explain what the inequality says about the buying and selling prices

c; if the store buys tshirts for 12$, what selling price range will make selling two tshirts more profitable that selling one shirt

 The kinetic energy of a moving object is related to its mass and velocity by the formula Ek=1/3mv^2, where Ek  is the kinetic energy in Jules, m is the mass of the object in kilograms, v is the objects velocity in metres per second.  what are the possible velocities for a 3kg object  with a kinetic energy of less than 600 J? ( negative velocities are acceptable and represent the opposite direction of a positive velocity)

Write a simplified expression in terms c, for the area of the given triangle.

c-1/c^2-c-12 

c+3/c^2-5c+4