Refer to right triangle ABC with C = 90 degrees if a=6 and c=18, find b

16.97

Step-by-step explanation:

To solve for a missing side in a right angles triangle, we solve using Pythagoras Theorem.

Pythagoras Theorem =

a² + b² = c²

Where c = Hypotenuse = Longest side

From the question above,

a=6 and c=18,

Hence,

6² + b² = 18²

b² = 18² - 6²

b² = 18² - 6²

b² = 324 - 36

b²= 288

Square root both sides

b = √288

b = 16.970562748

Approximately b ≈ 16.97

Given the graph of the function f(x) = (x - 4)(x + 1).

From the graph, it can be seen that the graph of the function describe a parabola facing up with the vertex at point (1.5, -6.25).
The x-intercepts of the graph are at points (-1, 0) and (4, 0) while the y-intercept is at point (0, -4)

The vertex of a parabola is the point in the parabola where the graph of the function stops decreasing and starts increasing, or vice-versa.

Thus, the function stops decreasing at point (1.5, -6.25) and then starts increasing, this means that for values of x < 1.5 the function is decreasing and since 0 < 1.5, hence, the function is decreasing for the values of x < 0. Hence, the statement that "the function is increasing for all real values of x where x < 0" is not true.

Similally, Given that the function stops decreasing at point (1.5, -6.5), this means that for values of x < 1.5 the function is decreasing and since -1 < 1.5, hence, the function is decreasing for the values of x < -1.
Thus, the statement that the function is increasing for all real values of x where x < –1 and where x > 4  is not true.

With the explanations given above, it can also be seen that the statement that "the function is decreasing for all real values of x where –1 < x < 4" is also not true.