Kamlu is on her balcony. Her friend is directly below her, tossing her an apple. He releases it from 5 feet above the ground with an initial velocity of 28 feet per second. If Kamlu's hands are 14 feet above the ground, how many chances will she get to catch the apple, and when? The following function models Kamlu's friend tossing the apple up to her.

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of StartFraction 8 x cubed minus 2 x squared minus 67 x minus 24 Over 2 x squared minus x minus 21 EndFraction?

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3