The height of a triangle is 4 in. greater than twice its base. the area of the triangle is no more than 168 in.2. which inequality can be used to find the possible lengths, x, of the base of the triangle?

The height (h) of a triangle is 4 in. greater than twice its base (x): h = 2x + 4
The area of the triangle is no more than 168 in.2: A ≤ 168 in²

The area of the triangle is A = x*h/2
Hence x*h/2 ≤ 168 in²

Substitute h in the formula for the area:
h = 2x + 4 = 2(x + 2)
x*h/2 ≤ 168 in²

x * 2(x + 2)/2 ≤ 168
x * (x + 2) ≤ 168
x² + 2x ≤ 168
x² + 2x - 168 ≤ 0

Using the formula for quadratic equation:

The boat's velocity relative to the riverbank can be resolved into two components. the component going north is 2.7 m/s and the component going west is 1.2 m/s.we add these two vectors and then find the magnitude of the resultant to get the speed.the magnitude of the resultant vector from adding can be obtained by the pythagorean theorem.    to two significant figures, the boat's speed relative to the riverbank is 3.0 m/s.