Aplane that carries mail makes a round trip each day from chicago to new york. it makes 2 intermediate stops on the way to new york and 3 intermediate stops on the way back to chicago. suppose you make a graph on the altitude of the plane for one day, whit time on the horizontal axis and altitude on the vertical axis. how many times will the graph touch the horizontal axis?

The graph touch the horizontal axis 8 times (two in Chicago, one in  New York, and five in the intermediate stops)

Step-by-step explanation:

At x = 0, the plane is in Chicago, so, the graph starts at y = 0, i. e., touching the horizontal axis; where y refers to altitude of the plane and x refers to time. Plane makes 2 intermediate stops on the way to New York; so, y = 0 two times before arrived to New York.  Also, in New York y = 0. Next, plane touch the horizontal axis 3 more times in the intermediate stops on the way back to Chicago. Finally y = 0 when the plane reach Chicago for the second time.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1