Answer:
<h2>A, B, D, E</h2>
Step-by-step explanation:
2(2x + 1) = (2)(2x) + (2)(1) = 4x + 2 → A
<em>used distributive property</em>
2(2x + 1) = 2(1 + 2x) → B
<em>used commutative property</em>
2(2x + 1) = (2x + 1) + (2x + 1) = 2x + 1 + 2x + 1 → D
<em>used 2a = a + a</em>
2(2x + 1) = 4x + 2 = x + x + x + x + 1 + 1 → E
<em>used 4x = x + x + x + x and 2 = 1 + 1</em>
The last one is The answer. Mark as Brainlest.
Hmm, the 2nd derivitve is good for finding concavity
let's find the max and min points
that is where the first derivitive is equal to 0
remember the difference quotient
so
f'(x)=(x^2-2x)/(x^2-2x+1)
find where it equals 0
set numerator equal to 0
0=x^2-2x
0=x(x-2)
0=x
0=x-2
2=x
so at 0 and 2 are the min and max
find if the signs go from negative to positive (min) or from positive to negative (max) at those points
f'(-1)>0
f'(1.5)<0
f'(3)>0
so at x=0, the sign go from positive to negative (local maximum)
at x=2, the sign go from negative to positive (local minimum)
we can take the 2nd derivitive to see the inflection points
f''(x)=2/((x-1)^3)
where does it equal 0?
it doesn't
so no inflection point
but, we can test it at x=0 and x=2
at x=0, we get f''(0)<0 so it is concave down. that means that x=0 being a max makes sense
at x=2, we get f''(2)>0 so it is concave up. that means that x=2 being a max make sense
local max is at x=0 (the point (0,0))
local min is at x=2 (the point (2,4))
Answer:
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
Step-by-step explanation:
The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Answer:
(22/5, 11/5)
Step-by-step explanation:
Gandalf starts walking in the vector v = 4i + 2j, the slope of it must be 2/4 = 1/2.
So, calling the turn point (x,y) it must be in that vector, and the start point (2,1) must also be in this line, so:
slope = Δy/Δx
1/2 = (y - 1)/(x - 2)
2y - 2 = x - 2
2y = x
y = x/2
The line that makes a right angle with another is called perpendicular, and it has its slopes equal to the opposite of the inverse of the slope of the other line, so:
slope = - 2
The point (x,y) also pertences to it, such as the point (3,5), so:
-2 = (y - 5)/(x - 3)
y - 5 = -2x +6
y = -2x + 11
So, the turn point is the point where these two lines meet:
x/2 = -2x + 11
x = -4x + 22
5x = 22
x = 22/5
y = (22/5)/2
y = 22/10 = 11/5
So, the point that he makes the turn is (22/5, 11/5).
