Midpoint = (x1 + x2) / 2, (y1 + y2)/2
(-2,1)....x1 = -2 and y1 = 1
(4,-1)...x2 = 4 and y2 = -1
time to sub
m = (-2 + 4) / 2 , (1 + (-1) / 2
m = (2/2), (0/2)
m = (1,0) <==
y = -x + 1.....(1,0)...x = 1 and y = 0
0 = -1 + 1
0 = 0 (correct)
so the midpoint M (1,0) lies on the line since its coordinates satisfy the equation <===
Answer:
g(x) = - (x² + 3x + 2) = - x² - 3x - 2
Step-by-step explanation:
The graph represents the function f(x) = x² + 3x + 2.
Now, g(x) is the function which is obtained by reflecting f(x) across the x-axis.
While a graph of a function reflects across x-axis then its y-values will change sign for a fixed value of x.
Therefore, the function g(x) will be given by
g(x) = - (x² + 3x + 2) = - x² - 3x - 2 (Answer)
Answer: What topic is this again??
Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
- If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.
- (Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.
If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
Answer:
-15
Step-by-step explanation:
