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Alexxx [7]
2 years ago
15

BD=BC, BD= 5x +26, BC= 2x+1, and AC = 43, find AB

Mathematics
1 answer:
Lostsunrise [7]2 years ago
8 0
Imagine that points A, B, C and D are collinear and appears in that order from the left to the right. You want to find the measure of the first line segment AB. First, let's find the value of x.

BD = BC
5x + 26 = 2x + 1
5x - 2x = 1 - 26
3x = -25
x = -8.33

2(-8.33) + 1 = -15.67
So, BD=BC= -15.67

To find AB, the solution is as follows:
AC = AB + BC
43 = AB + (-15.67)
AB = 58.67

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notice above, all we did, was isolate the "recurring part" to the right of the decimal point, so the repeating 09, ended up on the right of it.

now, let's say, "x" is a variable whose value is the recurring part, therefore then

\bf \cfrac{3659.0909\overline{09}}{1000}\qquad \boxed{x=0.0909\overline{09}} \qquad \cfrac{3659+0.0909\overline{09}}{1000}\implies \cfrac{3659+x}{1000}

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\bf \begin{array}{llllllll}
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\end{array}\quad \implies 100x=9+x\implies 99x=9
\\\\\\
x=\cfrac{9}{99}\implies \boxed{x=\cfrac{1}{11}}\\\\
-------------------------------\\\\
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\\\\\\
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and you can check that in your calculator.
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