Alright,
directix is y=something so it opens down or up
we use
(x-h)²=4p(y-k)
the vertex is (h,k)
and p is distance from focus to vertex
if focus is above directix, p is positive
if focus is below directix, p is negative
so we gts
focus=(1,1)
directix is y=-1
1>-1
focus is above
oh, vertex is in middle of focus and directix
so
beteeen (1,1) and y=-1 is, hmm
that is a distance of 2 vertically
2/2=1
1 down from (1,1) is (1,0)
vertex is (1,0)
p=1
so
(x-1)²=4(1)(y-0)
solving for y to get into f(x)=something form
(x-1)²=4y
y=1/4(x-1)²
f(x)=1/4(x-1)²
4th option
<span>Multiply one of the equations so that both equations share a common complementary coefficient.
In order to solve using the elimination method, you need to have a matching coefficient that will cancel out a variable when you add the equations together. For the 2 equations given, you have a huge number of choices. I'll just mention a few of them.
You can multiply the 1st equation by -2/5 to allow cancelling the a term.
You can multiply the 1st equation by 5/3 to allow cancelling the b term.
You can multiply the 2nd equation by -2.5 to allow cancelling the a term.
You can multiply the 2nd equation by 3/5 to allow cancelling the b term.
You can even multiply both equations.
For instance, multiply the 1st equation by 5 and the second by 3. And in fact, let's do that.
5a + 3b = –9
2a – 5b = –16
5*(5a + 3b = -9) = 25a + 15b = -45
3*(2a - 5b = -16) = 6a - 15b = -48
Then add the equations
25a + 15b = -45
6a - 15b = -48
=
31a = -93
a = -3
And then plug in the discovered value of a into one of the original equations and solve for b.</span>
Answer:
(y^2)/4 square meters
Step-by-step explanation:
For a perimeter length of x, the side of a square will be x/4 and its area will be (x/4)^2.
If one side of the square is shortened by y/2 and the adjacent side is lengthened by y/2, then the difference in side lengths will be y. The area of the resulting rectangle will be ...
(x/4 -y/2)(x/4 +y/2) = (x/4)^2 -(y/2)^2
That is, the difference in area between the square and the rectangle is ...
(x/4)^2 - ((x/4)^2 -(y/2)^2) = (y/2)^2 = y^2/4
The positive difference between the area of the square region and the area of the rectangular region is y^2/4 square meters.
Answer:
Step-by-step explanation:
I have 30 coins, all nickels, dimes, and quarters, worth $4.60. There are two more dimes than quarters. How many of each kind of coin do I have.
..
let quarters be x
dimes = x+2
...
dimes + quarters = x+x+2=2x+2
...
nickels = 30-(2x+2)
...
5(30-(2x+2))+10(x+2)+25x=460
5(30-2x-2)+10x+20+25x=460
150-10x-10+10x+20+25x=460
160+25x=460
-160
25x=460-160
25x=300
/25
x=300/25
x=12 ---- quarters
x+2= 12+2=14 dimes
30-(2x+2)=4 nickels
...
check
4*5+14*10+12*25=20+140+300=460
Answer: 8x+12
Step-by-step explanation:
We can use the Distributive Property to get it in it's simplest form
4(2x+3)
(4)(2x)+(4)(3)
8x+12
