A dolphin jumps out of the water. The function h=-16t^2+26t models the height (in feet) of the dolphin after t seconds. After how many seconds is the dolphin at a height of 5 feet.

The dolphin is five feet in the air after about 0.22 and 1.40 seconds.

Step-by-step explanation:

The height h (in feet) of the dolphin as it jumped out of the water after t seconds is given by the function:

We want to determine the time(s) when the dolphin is five feet in the air.

Since the dolphin is five feet in the air, h(t) = 5:

Solve for t. Rearrange:

We can use the quadratic formula, given by:

In this case, a = 16, b = -26, and c = 5.

Substitute:

Evaluate:

Simplify the square root:

Hence:

Simplify:

Hence, our solutions are:

The dolphin is five feet in the air after about 0.22 and 1.40 seconds.

(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

-1/2 +2

step-by-step explanation: