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Maru [420]
3 years ago
5

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

Mathematics
2 answers:
exis [7]3 years ago
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

so

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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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther
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<h2>Answer:</h2>

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a_{n}=a_{n-1}+(n-1)^{2}

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\

Therefore, on checking, we observe that,

a_{n}=a_{n-1}+(n-1)^{2}

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0

which is true.

<u>At, </u>

<u>n = 2</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1

Which is also true.

<u>At, </u>

<u>n = 3</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5

Which is true.

<u>At, </u>

<u>n = 4</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

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