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3 years ago

If B is the midpoint of AC, and AC=8x-20. Find BC AB=3x-1 Show all work

2 answers:

6 0

First we know that:
AB+BC=AC
now , since B is the midpoint of AC, this means that AB=BC
therefore,
AB+BC=AC can also be written as
AB+AB=AC
3x-1+3x-1=8x-20
6x-2=8x-20
-2+20=8x-6x
18=2x
x=9

therefore:
AB=3(9)-1=27-1=26
AC=8(9)-20=52
BC=AB=26

lesantik [10]3 years ago

4 0

Answer:

$BC=26$

Step-by-step explanation:

we know that

$AC=AB+BC$ -----> equation A

In this problem

B is the midpoint of AC

$AB=BC$ ------> equation B

substitute equation B in equation A

$AC=AB+AB$ ------> $AC=2AB$ ------> equation C

we have

$AC=8x-20$

$AB=3x-1$

substitute the values in equation C and solve for x

$8x-20=2(3x-1)$

$8x-20=6x-2$

$8x-6x=20-2$

$2x=18$

$x=9$

Find AB

$AB=3x-1=3(9)-1=26$

Remember that

$AB=BC$

therefore

$BC=26$

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<img src="https://tex.z-dn.net/?f=81-%28y-1%29%28y%5E2%2B27%29%20%5Cgeq%200%20%5C%5C%5C%5C%2081-%28y%5E3%2B27y-y%5E2-27%29%20%5C

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The other method is using Newton's method, it is similar to this but with a twist because it involves differentiation, so $y_{n+1}=y_n-\frac{f(y)}{f'(y)}$ where 'n' is the number you approximate, like n=0,1,2... etc. f(y) would the equation, and f'(y) is the derivative of f(y), now what you'll need to do is substitute the 'n' values into 'y' to find the approximation.