Get it in form 4P(y-k)=(x-h)^2
add 8y to both sides
x^2-6x+49=8y
complete the square
-6/3=-3, (-3)^2=9
(x^2-6x+9)+40=8y
(x-3)^2+40=8y
minus 40 both sides
(x-3)^2=8y-40
undistribute 8 on right side
(x-3)^2=(y-5)8
4P(y-k)=(x-h)^2
4(2)(y-5)=(x-3)^2
(h,k) is center
p is distance from vertex to directix and also from vertex to focus
p=2
vertex=(3,5)
in that form, the prabola opens up so
directix is 2 below vertex
focus is 2 above vertex
up and down is y so
5-2=3
5+2=7
directix is y=3
focus=(3,7)
vertex=(3,5)
Answer: n = 4
Step-by-step explanation:
The given expression is
2n+4=12
We want to solve for n. The first step is to make 2n stand alone on the left hand side of the equation. This is achieved by subtracting 4 from the left hand side and the right hand side of the equation. It becomes
2n + 4 - 4=12 - 4
2n = 8
The next step is to divide the left hand side and the right hand side of the equation by 2. It becomes
2n/2 = 8/2
n = 4
Answer:
35
Step-by-step explanation:
35 is not divisible by 3 as all the other numbers are
Answer:
f(g(7)) = 22
Step-by-step explanation:
First find the general form of the new equation, f(g(x)):
f(x)=3x + 2
g(x)=x - 1/3
f(g(x)) = 3(x - 1/3) + 2
You can simplify that, or alternatively just plug in 7 now and solve:
f(g(7)) = 3(7 - 1/3) + 2
f(g(7)) = 3(20/3) + 2
f(g(7)) = 20 + 2
f(g(7)) = 22
<em>Answer:</em>
<em>(69,979)</em>
<em>Step-by-step explanation:</em>
<em>In the coordinates, x is represented as 69. We can now insert this into the equation.</em>
<em>y = 13x + 82</em>
<em>Now to insert x.</em>
<em>y = 13(69) + 82</em>
<em>Now we can multiply 13 by 69.</em>
<em>13*69 = 897</em>
<em>Now fix the equation.</em>
<em>y = 897 + 82</em>
<em>Now add to get our y.</em>
<em>897 + 82 = 979</em>
<em>Substitute into the equation.</em>
<em>y = 979</em>
<em>And there is our answer. We now need to put this into the coordinates.</em>
<em>And we get our final answer of (69,979).</em>
<em>Hope this helps. Have a nice day.</em>
