Answer: the answer is 10
Step-by-step explanation:
1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.
No. It's the ratio of 1,289 to 100 .
Also, it can be written as a fraction with whole numbers
on top and bottom, like this: 1289 / 100 .
Also, it can be written down on paper completely, using
digits and a decimal point or fraction bar. (You did that.)
Any one of these three facts makes it a rational number.
Answer:
Step-by-step explanation:
Given: The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
To find: coordinates of vertex of the right angle
Solution:
Let C be point 
Distance between points 
is given by 
ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)
![34=\left [ (x-4)^2+(y-1)^2 \right ]+\left [ (x+1)^2+(y+2)^2 \right ]](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%28x-4%29%5E2%2B%28y-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%28x%2B1%29%5E2%2B%28y%2B2%29%5E2%20%5Cright%20%5D)
Put 
![34=\left [ (-1-4)^2+(1-1)^2 \right ]+\left [ (-1+1)^2+(1+2)^2 \right ]\\34=25+9\\34=34](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%28-1-4%29%5E2%2B%281-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%28-1%2B1%29%5E2%2B%281%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D25%2B9%5C%5C34%3D34)
which is true. So, 
can be a vertex
Put 
![34=\left [ (4-4)^2+(-2-1)^2 \right ]+\left [ (4+1)^2+(-2+2)^2 \right ]\\34=9+25\\34=34](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%284-4%29%5E2%2B%28-2-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%284%2B1%29%5E2%2B%28-2%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D9%2B25%5C%5C34%3D34)
which is true. So, 
can be a vertex
Put 
![34=\left [ (1-4)^2+(1-1)^2 \right ]+\left [ (1+1)^2+(1+2)^2 \right ]\\34=9+4+9\\34=22](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%281-4%29%5E2%2B%281-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%281%2B1%29%5E2%2B%281%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D9%2B4%2B9%5C%5C34%3D22)
which is not true. So, 
cannot be a vertex
Put 
![34=\left [ (2-4)^2+(-2-1)^2 \right ]+\left [ (2+1)^2+(-2+2)^2 \right ]\\34=4+9+9\\34=22](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%282-4%29%5E2%2B%28-2-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%282%2B1%29%5E2%2B%28-2%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D4%2B9%2B9%5C%5C34%3D22)
which is not true. So, 
cannot be a vertex
Put 
![34=\left [ (4-4)^2+(-1-1)^2 \right ]+\left [ (4+1)^2+(-1+2)^2 \right ]\\34=4+25+1\\34=30](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%284-4%29%5E2%2B%28-1-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%284%2B1%29%5E2%2B%28-1%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D4%2B25%2B1%5C%5C34%3D30)
which is not true. So, 
cannot be a vertex
Put 
![34=\left [ (-1-4)^2+(4-1)^2 \right ]+\left [ (-1+1)^2+(4+2)^2 \right ]\\34=25+9+36\\34=70](https://tex.z-dn.net/?f=34%3D%5Cleft%20%5B%20%28-1-4%29%5E2%2B%284-1%29%5E2%20%5Cright%20%5D%2B%5Cleft%20%5B%20%28-1%2B1%29%5E2%2B%284%2B2%29%5E2%20%5Cright%20%5D%5C%5C34%3D25%2B9%2B36%5C%5C34%3D70)
which is not true. So, 
cannot be a vertex
So, possible points for the vertex are
I don’t understand. Could you break the question down?
