9514 1404 393
Answer:
x = -1, 1, 9
Step-by-step explanation:
You want x such that f(x) = g(x). Subtracting g(x) from both sides of this equation lets us rewrite it as ...
f(x) -g(x) = 0
x³ -9x² -(x -9) = 0
x²(x -9) -1(x -9) = 0 . . . factor the first pair of terms
(x² -1)(x -9) = 0 . . . . . . use the distributive property
(x -1)(x +1)(x -9) = 0 . . . . factor the difference of squares
Values of x that make these factors zero will make f(x) = g(x):
x = -1, 1, 9 for f(x) = g(x)
The triangle that forms is a right-angled triangle. To work out the area, you just do the base × height, all divided by 2.
Therefore, you do 5 (the base) × 4 (the height) and you get 20.
Then you divide by 2 to finish the equation and you should find that the total area of the triangle is 10 units² (20 ÷ 2 = 10).
Hope that helps :)
