The parabola is a sideways parabola....to intersect at only one point ist must intersect at the vertex
-y^2 -3y - 5 = x
y^2 + 3y+5 = -x
(y+1.5)^2 + 2.75 = -x
x = (-1)(y+1.5)^2 - 2.75
the x point of the vertex is - 2.75 x =- 2.75
Base from 1,3 to 3,0 is sqrt 13
Height fro 3,1 to 6,6 is sqrt34
1/2 sqrt 34 * sqrt 13 = 1/2 (sqrt 442) = 10.51 units^2
The sum of any two sides of a triangle must be greater than the the remaining side
x+25 must be greater then 80
x = 56
Similar Q with good answer to follow by textot....
https://web2.0calc.com/questions/pls-help_2505
11 is 4 / 6 of the way from x = 15 to x = 9 4/6 to 2/6 = 2:1 (or 1:2 going the other direction)
4/6 of the way from 5 to 20 is 15 = y
https://web2.0calc.com/questions/any-help-is-appreciated_5
(9 x 10⁹ Nm²/C²) (3C) (6C)/10 N note that the C's and the 'N' will cnacel and the final result will be m^2
9 x 109 * 18/10 = 9 x 109 * 1.8 = 16.2 x 109 = 1.62 x 1010 m2
p= total number of pens originally
sell 1/2 then 1/2 remain
p - 1/2 p -30 = pens after Tuesday
(p- 1/2 p - 30) 2/3 = pens after Wednesday and this = 40 that were sold on Thursday
(p-1/2p-30)2/3 = 40
(1/2 p-30)(2/3) = 40
1/3 p - 20 = 40
1/3 p = 60
p = 180 pens
acid in ingredients = acid in final sol'n
x = 25% gallon amount
.25 x + .12 (10) = .20 (10+x)
.05x = .8
x = 16 gal of 25%
Just add and subtract them as indicated
2x^2 + 3x -9 - 5x - 11 + 3x^2 +1 gather 'like' terms
5x^2 -2x -19