x + y when x = 6 and y = 2
6 + 2 = 8
when x = 12 and y = 20
= 37
when m = 12 and n = 3
= 24
Six times x
6x
Six increased by x
6 + x
The sum of x and y
x + y
1)We need to know the amount of yellow tint in the old mixture.
amount of yellow tint=30% of 40 liters
30%=30/100=0.3
Amount of yellow tint=0.3(40 liters)=12 liters.
2)We need to find the amount of yellow tint in the new mixture.
amount of yellow tint in the new mixture=12 liters + 9 liters=21 liters.
3) we calculate the amount of the new mixture:
amount of new mixture=40 liters + 9 liters=49 liters
4) we compute the percent of yellow tint in the new mixture:
percent of yellow tint =(amount of yellow tint / amount of mixture)*100
percent of yellow tint=(21 liters / 49 liters)100≈42.9%
Answer: The percent of yellow tint in the new mixture is 42.9%.
note: if this answer is not correct you can try it with 42.8%
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:
7
— or -1.75
-4
Explanation:
Let’s do the y2-y1/x2-x1 strategy! The equation will be 5+2/-6+2. To simplify, it will be 7/-4. So -1.75 or 7/-4 should be the slope. SCan you make me brainliest? Thank you if you do. Have a good day!