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Gala2k
2 months ago
5

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

Mathematics
2 answers:
Leona [12.6K]2 months ago
6 0
Let's begin with:
AB + BC = AC
Since B divides AC exactly in half, we know AB equals BC.
Hence,
AB + BC = AC translates to
AB + AB = AC
or
3x - 1 + 3x - 1 = 8x - 20
Simplify:
6x - 2 = 8x - 20
Add 20 to both sides and subtract 6x:
18 = 2x
Divide both sides by 2:
x = 9

Therefore:
AB = 3(9) - 1 = 27 - 1 = 26
AC = 8(9) - 20 = 52
BC = AB = 26
babunello [11.8K]2 months ago
4 0

Answer:

BC=26

Step-by-step explanation:

We start with the fact that

AC=AB+BC (equation A)

In this problem,

B is the midpoint of AC,

which means

AB=BC (equation B)

Substituting equation B into equation A gives

AC=AB+AB leading to AC=2AB (equation C)

We have:

AC=8x-20

AB=3x-1

Replacing values in equation C and solving for x results in

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

8x-20=6x-2

8x-6x=20-2

2x=18

x=9

Next, calculate AB:

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

Recall that

AB=BC

Therefore,

BC=26

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Joaquin is four more than half Marjorie’s age. Marjorie is also 32 less than three times Joaquin’s age.
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Answer:

Her age is 40 years

Step-by-step explanation:

Let Jerry's age be represented as j

Let Marjorie's age be denoted as m

The first part of the question states:

j = 4 + m/2

For the second equation:

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Multiply the first equation by 2 to get:

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By simplifying, we get:

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Therefore, j = 24

Now substituting back:

m = 2j - 8

m = 2(24) - 8

Thus, m = 48 - 8

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