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If: y = x^2+4 and y = 5x+10

Then: x^2+4 = 5x+10

So: x^2-5x-6 = 0 => x = -1 or x = 6

Points of intertsection by substitution: (6, 40 and (-1, 5)

Length of line: sq rt of (6--1)^2+(40-5)^2 = 7 times sq rt 26 or 35.693 to 3 d.p.

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Q: What are the points of intersection of the line y equals 5x plus 10 that spans the parabola y equals x squared plus 4 and its length?
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What is the length of the line of y equals 17-3x that spans the parabola of y equals x squared plus 2x -7 showing work and answer to three decimal places?

If: y = 17-3x and y = x^2+2x-7 Then: x^2+2x-7 = 17-3x => x^2+5x-24 = 0 Solving the quadratic equation: x = -8 and x = 3 Points of intersection with the parabola: (-8, 41) and (3, 8) Length of line: square root of [(-8-3)^2+(41-8)^2] = 34.785 to 3 d.p.


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Equations: x2+2x-7 = 17-3x Quadratic equation: x2+5x-24 = 0 Points of intersection: (-8, 41) and (3, 8) Length of line: (-8-3)2+(41-8)2 = 1210 and the square root of this is the length of the line which is about 34.78505426 or to be exact it is 11 times the square root of 10.


What is the length of the line y equals 17 -3x that spans the parabola y equals x squared plus 2x -7 showing work?

If: y = x^2 +2x -7 and y = 17 -3x Then: x^2 +2x -7 = 17 -3x => x^2 +5x -24 = 0 Solving the equation: x = 3 or x = 8 Points of intersection: (3, 8) and ( -8, 41) Length of line: square root of 1210 which is about 34.785 to three decimal places


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Related questions

What is the length of the line of y equals 5x plus 10 that joins the parabola of x squared plus 4 at two points?

It works out exactly as: 7 times the square root of 26


If A squared plus B squared equals C squared and C equals 8 and A and B are the same length what are A and B?

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What is the length of the line of y equals 17-3x that spans the parabola of y equals x squared plus 2x -7 showing work and answer to three decimal places?

If: y = 17-3x and y = x^2+2x-7 Then: x^2+2x-7 = 17-3x => x^2+5x-24 = 0 Solving the quadratic equation: x = -8 and x = 3 Points of intersection with the parabola: (-8, 41) and (3, 8) Length of line: square root of [(-8-3)^2+(41-8)^2] = 34.785 to 3 d.p.


What is the length of the line of y equals 17-3x that spans the parabola of y equals x squared plus 2x -7 showing work?

First find the points of intersection of the two equations: 17 - 3x = x2 + 2x - 7 or x2 + 5x - 24 = 0 This has the solutions x = 3 and x = -8 So the coordinates of the two points of intersection are (3,8) and (-8,41). Then, by Pythagoras, the length is sqrt[(3+8)2 + (8-41)2] = sqrt(121 + 1089) = sqrt(1210) = 11 sqrt(10) or 34.785 units (approx).


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