4y^2 - 8y + 25x^2 +150x - 171 = 0
4y^2 - 8y + 25x^2 +150x - 171 = 0 Rearrange and regroup.
(25x^2 + 150x) + (4y^2 - 8y) = 0+171. Group the xs together and the ys together.
25(X^2 + 6x) + 4(y^2-2y) = 171. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 6.
Half of it = 1/2 * 6 = 3. (Note this value)
Square it = 3^2 = 9. (Note this value)
Coefficient of y in the second expression = -2.
Half of it = 1/2 * -2 = -1. (Note this value)
Square it = (-1)^2 = 1. (Note this value)
We are going to carry out a manipulation of completing the square with the values
9 and 1. By adding and substracting it.
25(X^2 + 6x) + 4(y^2-2y) = 171.
25(X^2 + 6x + 9 -9) + 4(y^2-2y + 1 -1) = 171
Note that +9 - 9 = 0. +1 -1 = 0. So the equation is not altered.
25(X^2 + 6x + 9) -25(9) + 4(y^2-2y + 1) -4(1) = 171
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1) Transferring the terms -25(9) and -4(1)
to other side of equation.
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1)
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 400
We now complete the square by using the value when coefficient was halved.
25(x+3)^2 + 4(y-1)^2 = 400
Divide both sides of the equation by 400
(25(x+3)^2)/400 + (4(y-1)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x+3)^2)/16 + ((y-1)^2)/100 = 1
((x+3)^2)/(5^2) + ((y-1)^2)/(10^2) = 1
Comparing to the general format of an ellipse.
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Coordinates of the center = (h,k).
Comparing with above (x+3) = (x - h) , h = -3.
Comparing with above (y-1) = (y - k) , k = 1.
Therefore center = (h,k) = (-3, 1).
You can easily draw the ellipse...Cheers.
She can 18 because 40.00 divided by 2.50 is 18 :)
Hey there!
First, we'll solve for x = 0.
The first step is to replace x with 0 anytime it appears in the equation.
f(0) = 7(0) + 2
Multiply 7 by 0 next because multiplication comes before addition in PEMDAS.
f(0) = 0 + 2
Then, add 2 to 0 since it is the last step.
f(0) = 2 The value of f(x) when x = 0 is 2.
Now we can solve for x = 1.
The first step is to replace x with 1 anytime it appears in the equation.
f(1) = 7(1) + 2
Multiply 7 by 1 next because multiplication comes before addition in PEMDAS.
f(1) = 7 + 2
Then, add 2 to 7 because it is the last step.
f(1) = 9 The value of f(x) when x = 1 is 9.
Hope this helps!
First we have to find how much they spent on each gallon.
To find out how much Carly paid for each gallon we have to divide her total price by haw many gallons she got.
$17.50/7=$2.50 per gallon
Likewise we do the same for Jade
$45/15=$3
So the answer will be Jade paid more per gallon than Carly