Looks like Chris is signed off presently.....
Looking for b ?
a^2 = b^2 + c^2
a = 58 (million miles)
c = 12 (million miles)
58^2 = b^2 + 12^2
b = 57 million miles
Use T = time in SECONDS
G = gravitational constant 6.67408 x 10-11
M = mass of Sun 1.989 x 1030
And the equation T = sqrt (4 pi2 r3 /(GM) ) Solve for r which will be in METERS
Then divide by AU (in meters ) 1.4959787 x 1011 Let me know what ya find for an answer.....it IS in your list of possibles !
f(x) = y = 100 x
The shortest one is 2 m 2m x 100cm/m = 200 cm
similarly the other two are 300 cm and 400 cm
domain would be the lenghts 2 <= x <= 4
Range would be the cm lengths 200<=y<=400
Let's put the circle in standard form
x^2 + 4x +y^2 -6y = 3 now 'complete the square'on x and y
(x+2)*2 + (y-3)^2 = 3 +4+9
(x+2)^2 + (y-3)^2 = 4^2 so the center is (a,b) = (-2,3) and the radius is 4 a+b+r = 5
Here is a graph of the rectangle (the 4th corner is 5,-2) and the equation of the circle....
I think you can see the area in question is 1/4 the area of the circle:
https://www.desmos.com/calculator/eno5sm5r56
= [3(-2)]2 - 4(-3)2
= 36 - 4(9) = 0
Chris just forgot the -g(x) portion of f(x)
so he got 9 fpr the first part...
9 - (2(3)-1)
9-6+1 = 4
If (x+4) is a factor, then x+4 = 0 so x= -4
if you put -4 into the origianl equation (this would be f(-4) ) and get any other number besides 0 , then (x+4) is not a factor.....
can you figure this out now?
Initial location -4,9
final location -14, 2 (10 units left 7 units down)
Now you have two points on a line......let's see....do you remember how to find the slope between these two points?
Subtract " 3x4 +2x-1 " from both sides of the equation.....and the left side will be left with only h(x) =...........