16x^2 + 25y^2 + 160x - 200y + 400 = 0 Rearrange and regroup.
(16x^2 + 160x) + (25y^2 - 200y ) = 0-400. Group the xs together and the ys together.
16(X^2 + 10x) + 25(y^2-8y) = -400. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 10.
Half of it = 1/2 * 10 = 5. (Note this value)
Square it = 5^2 = 25. (Note this value)
Coefficient of y in the second expression = -8.
Half of it = 1/2 * -8 = -4. (Note this value)
Square it = (-4)^2 = 16. (Note this value)
We are going to carry out a manipulation of completing the square with the values
25 and 16. By adding and substracting it.
16(X^2 + 10x) + 25(y^2-8y) = -400
16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400
Note that +25 - 25 = 0. +16 -16 = 0. So the equation is not altered.
16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = -400 +16(25) + 25(16) Transferring the terms -16(25) and -25(16)
to other side of equation. And 16*25 = 400
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 25(16)
16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 400
We now complete the square by using the value when coefficient was halved.
16(x-5)^2 + 25(y-4)^2 = 400
Divide both sides of the equation by 400
(16(x-5)^2)/400 + (25(y-4)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x-5)^2)/25 + ((y-4)^2)/16 = 1
((x-5)^2)/(5^2) + ((y-4)^2)/(4^2) = 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-5) = (x - h) , h = 5.
Comparing with above (y-k) = (y - k) , k = 4.
Therefore center = (h,k) = (5,4).
Sorry the answer came a little late. Cheers.
Answer:
<h3>B. m∠R = 110°, m∠T = 110°, m∠U = 70°</h3>
Step-by-step explanation:
The opposite angles of the parallelogram are the same.
From the diagram;
<S = <U and <R = <T
Given
<S = 70°
Since <S = <U, hence <U = 70°
Since the sum of angles in a quadrilateral is 360 degrees, hence;
<R+<S+<T+<U = 360
Since <R = <T, then;
<Y+<S+<T+<U = 360
2<T + 70+70 = 360
2<T = 360-140
2<T = 220
<T = 220/2
<T = 110°
Since <T = <R, then < R = 110°
Hence m∠R = 110°, m∠T = 110°, m∠U = 70°. Option B is correct
Answer: 2
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
1. The inverse means take the not of both sides
If it is Saturday, then there is no school.
Inverse If it is not Saturday, then there is school.
The converse flips the then and the if
If there is no school, then it is Saturday.
2.) The first given part is the if, what will happen is the then part
If you are a freshman, then you are required to attend orientation.
3.)
Given: 3x+1=-14 Prove: x=-5
Statements Reasons
1. 3x+1=-14 Given
2. 3x=-15 Subtraction Property of equality ( since we subtract 1 from each side)
3. X=-5 Division Property ( since we divide each side by 3)
Answer:
-8 and 6
Step-by-step explanation:
he spent 8 on the book, therefore he had deduced 8 dollars, and earned 6, therefore he had increased 6 dollars
