12x - 5(2x - 6) = 30 12 x - 10x + 30 = 30 2x = 0, x = 0 y = -6
If: y = 3x^2 +10x +11 and y = 2 -2x -x^2 Then: 3x^2 +10x +11 = 2 -2x -x^2 Transposing terms: 4x^2 +12X +9 = 0 Factorizing the above: (2x+3)(2x+3) = 0 meaning x = -3/2 By substitution into original equations intersection is at (-3/2, 11/4)
If: y = 2 -2x -x^2 and y = 3x^2 +10x +11 Then: 3x^2 +10X +11 = 2 -2x -x^2 Or: 4x^2 +12x +9 = 0 Factorizing the above: (2x+3)(2x+3) = 0 meaning x = -3/2 When x = -3/2 then by substitution y = 11/4 Therefore point of contact is at: (-3/2, 11/4)
I assume you mean...,12X - 5Y = 30Y = 2X - 6You are given Y, so insert it into the top equation above.12X - 5(2X - 6) = 3012X - 10X + 30 = 302X = 0X = 0=====so, obviously,Y = - 6======Check.12(0) - 5(- 6) = 3030 = 30========checks(0, - 6)=======Ordered pair.
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
10x+2x-3y-4y=12x-7y
12x - 5(2x - 6) = 30 12 x - 10x + 30 = 30 2x = 0, x = 0 y = -6
Substitute 2x - 6 for y in first equation: 12x - 5(2x - 6) = 30 ie 12x - 10x + 30 = 30 so 2x = 0 making x = 0 and y = -6
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If: y = 3x^2 +10x +11 and y = 2 -2x -x^2 Then: 3x^2 +10x +11 = 2 -2x -x^2 Transposing terms: 4x^2 +12X +9 = 0 Factorizing the above: (2x+3)(2x+3) = 0 meaning x = -3/2 By substitution into original equations intersection is at (-3/2, 11/4)
If: y = 3x^2 +10x +11 and y = 2 -2x -x^2 Then: 3x^2 +10x +11 = 2 -2x -x^2 Transposing terms: 4x^2 +12x +9 = 0 Factorizing: (2x +3)(2x +3) = 0 => x = -3/2 and also x = -3/2 Therefore by substituting the point of contact is at: (-3/2, 11/4)
20x2 + 22xy + 6y2 = 20x2 + 10xy + 12xy + 6y2 = 10x(2x + y) + 6y(2x + y) = (2x + y)(10x + 6y) = 2(2x + y)(5x + 3y)
If: y = 2 -2x -x^2 and y = 3x^2 +10x +11 Then: 3x^2 +10X +11 = 2 -2x -x^2 Or: 4x^2 +12x +9 = 0 Factorizing the above: (2x+3)(2x+3) = 0 meaning x = -3/2 When x = -3/2 then by substitution y = 11/4 Therefore point of contact is at: (-3/2, 11/4)
Oh, what a lovely little math problem we have here! Let's take a deep breath and simplify this together. We can factor out a 2x from the first two terms and a 3 from the last two terms, leaving us with 2x(y-5) + 3(y-5). Now, we can see that we have a common factor of (y-5), so our final answer is (2x+3)(y-5). Great job working through that!
I assume you mean...,12X - 5Y = 30Y = 2X - 6You are given Y, so insert it into the top equation above.12X - 5(2X - 6) = 3012X - 10X + 30 = 302X = 0X = 0=====so, obviously,Y = - 6======Check.12(0) - 5(- 6) = 3030 = 30========checks(0, - 6)=======Ordered pair.
its just a line, there are many answers that would work -12x-6y=0 -12x=6y x=-y/2 y=-2x
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2