Answer:
Step-by-step explanation:
If the lines are parallel, it means that the slopes are the same. To write an equation in the slope intercept form, we need the slope and the y-intercept. We are given the slope. We need to find the y-intercept. We can use the slope and the point to help us. The point is written in the form (x,y). In this case the point is (2,4) so we will use 2 for x and 4 for y.
y = mx + b Plug in what we know
4 = -4(2) + b b is what we are looking for. It is the y-intercept
4 = -8 + b Now add 8 to both sides
12 = b
Now we can write the equation:
y = -4x +12
9. y=-1/4x^2+4x-19
group
y=(-1/4x^2+4x)-19
undistribute -1/4
y=-1/4(x^2-16x)-19
take 1/2 of -16 and squer it to get 64 then add neg and pos inside
y=-1/4(x^2-16x+64-64)-19
factorperfect square
y=-1/4((x-8)^2-64)-19
expand
y=-1/4(x-8)^2+16-19
y=-1/4(x-8)^2-3
vertex is (8,-3)
10.
group
y=(1/4x^2-3x)+18
undistribute
y=1/4(x^2-12x)+18
take 1/2 of -12 and square it and add neg and pos isndie
y=1/4(x^2-12x+36-36)+18
factor
y=1/4((x-6)^2-36)+18
expand
y=1/4(x-6)^2-9+18
y=1/4(x-6)^2+9
get to form (x-h)^2=4p(y-k)
minus 9 both sides and times 4
(x-6)^2=4(y-9)
(x-6)^2=4(1)(y-9)
so 1>0 so opens up and focus is 1 above vertex
vertex is (6,9)
so focus i (6,10)
11.
y=(-1/6x^2+7x)-80
y=(-1/6)(x^2-42x)-80
take 1/2 of linear coefient and squer it and add negative and positive inside
-42/2=-21, (-21)^2=441
y=(-1/6)(x^2-42+441-441)-80
factor perfect square the square
y=(-1/6)((x-21)^2-411)-80
expand
y=(-1/6)(x-21)^2+73.5-80
y=(-1/6)(x-21)^2-6.5
add 6.5 to both sid
y+6.5=(-1/6)(x-21)^2
times both sides by -6
-6(y+6.5)=(x-21)^2
(x-21)^2=-6(y+6.5)
(y-21)^2=4(-3/2)(y-(-6.5))
vertex is
-3/2<0 so directix is above
it is -3/2 or 1.5 units above the vertex
up is y so
-6.5+1.5=-5
the directix is y=-5
11.
in form (y-1)^2=4p(x+3)
opens left or right
(y-1)^2=4(4)(x+3)
vertex is (-3,1)
4>0 so opens right
dirextix is to left
it is 4 units to left
(-3,1)
left right is x
4 left of -3 is -4-3=7
x=-7 is da directix
The midpoints of the sides are:
M ( (2a+0)/2 , (2b+0)/2 ) = ( a , b )
N ( (-2a+0)/2 , (2b+0)/2 ) = ( - a, b )
P ( (-2a+0)/2, ( -2b+0)/2 ) = ( - a, - b )
Q ( (2 a+0)/2) , (-2b+0)/2 ) = ( a , - b )
The midpoints of a rhombus determine a rectangle.
64%. Not a random number. I did it with this tool I programmed on my own, but BE WARNED it is still buggy so this answer might not be correct. I will send the tool when it's 100% done if you want :)
