Answer: 4x√5
Step-by-step explanation:
√2x • √40x=
√(2*40*x*x)=
√80x^2=
√(16*5x^2)=4x√5
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)
I was expecting a choice that said A(1,4) is in the first quadrant so 90 degrees clockwise is fourth quadrant. For perpendicularity we reverse the coordinates, negating one of them. For the fourth quadrant, it must be the y coordinate that's negative. We end up at A'(4,-1).
The answer is the second choice: create a circle with the center at the origin. The image of A' will be on the circle, 90 degrees clockwise from A.
Answer:
(-2 2/3,0)
(0,2)
Step-by-step explanation:
Just did it
Answer:
-7π/3 or -420 degrees
Step-by-step explanation:
So we know that the arrow has made one full rotation and that it is moving in a clockwise direction. So already we have -2π degrees.
The arrow stops at π/6 before the next π/2 rotation. Therefore we find the difference between the two.
π/2 - π/6
3π/6 - π/6 = 2π/6
π/3
Since this is still clockwise, we make this negative. So the measure of the angle shown by the arrow is -2π - π/3
