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3 years ago

What is the vale of x?

Mathematics

2 answers:

dimaraw [331]3 years ago

4 0

Since the triangles are similar, the following is true:

20 x+6
------- = -------
2x -6 36

Then (20)(36) = (x+6)(2)(x-3) = 2[x^2+3x-18], or

720 = 2[x^2+3x-18], or 360 = x^2 + 3x - 18.

Then x^2 + 3x - 18 - 360 = 0. This is a quadratic equation which can be solved using the quadratic formula, among other approaches. Please apply the quadratic formula here, using a=1, b=3 and c= -378, to find x.

sertanlavr [38]3 years ago

4 0

Since they are similar
36/x+6=2x-6/20

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jarptica [38.1K]

First, find slope of point A and B using slope formula:
y2-y1 = 7-0 = -7
x2-x1 3-8 5

Next, use the point-slope formula to find the equation (pick either point A or B to substitute into this equation; the answer will be the same either way):
y-y1=m(x-x1)
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y=-7x +56 so the y-intercept is 56. Hurray! Part 1 down!
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Now to answer part 2. Since AB ll CD, they have the same slope: -7
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Therefore, you can use the handy point-slope equation to calculate the equation of line CD. (Remember you only need one of the points to use this equation if you already have the slope.) Since the only point given is D(5,5), we'll use that one:
y-y1=m(x-x1)
y-5=-7(x-5)
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y=-7x + 12 Yay! That's the answer to part 2; the equation of line CD
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