The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the height above water and x is the horizontal distance in feet. if a beam of light is shone upward at an angle modeled by the equation x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?

5 feet

Step-by-step explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

where y is the height above water and x is the horizontal distance in feet.

If a beam of light is shone upward at an angle modeled by the equation

A beam of light hit the dolphin.

So, line must be intersect path of dolphin.

Using substation method,

Substitute y=10-x into dolphin equation.

Hence, The beam hit dolphin at 5 feet.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)