Answer:
(x + 1) (3 x^2 + 1)
Step-by-step explanation:
Factor the following:
3 x^3 + 3 x^2 + x + 1
Factor terms by grouping. 3 x^3 + 3 x^2 + x + 1 = (3 x^3 + 3 x^2) + (x + 1) = 3 x^2 (x + 1) + (x + 1):
3 x^2 (x + 1) + (x + 1)
Factor x + 1 from 3 x^2 (x + 1) + (x + 1):
Answer: (x + 1) (3 x^2 + 1)
In both cases you may well benefit from graphing the functions.
Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).
Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.
Thus the range includes all real numbers: (-infinity, infinity).
Since it forms a "right triangle" we can apply trigonometry.
sin x = oppo/hyp
sin x = 13/20
x = sin^-1(13/20)
x = sin^-1(0.65)
x = 40.5
rounded to nearest degree
x = 41 degrees
Hope this helps! :)
95x=85x+288
You could add 288 to any side, it just shows that they're 288 miles apart.
Let's subtract 85x from both sides.
10x=288
28.8=x
It'll take 28.8 hours for the trains to meet. Let's make sure.
28.8×95
2,736
28.8×85
2,448
2,736-2,448
288
So, they'll meet up after 28.8 miles.
Answer:
D
Step-by-step explanation:
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