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zlopas [31]
3 years ago
13

Point B is on line segment AC. Given AB = 4x – 6, AC = 2x + 10, and

Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

Answer:

AC=22

Step-by-step explanation:

If point B in somewhere along a segment between the points A and C, then it means that AB + BC = AC.

A---------------------------------C

A------------B-------------------C

     AB      +        BC       = AC

This means that we can write an equation:

4x-6(AB) + 4(BC) = 2x+10 (AC)

Which we can now solve for x:

(4x-6)+4=2x+10

Take out of brackets:

4x-6+4=2x+10

Combine like terms:

4x-2=2x+10

Move x terms to one side and other terms to the other:

4x-2x=10+2

Combine:

2x=12

Solve:

x=6

Now we can just substitute the x into the original AC equation to find its numerical length:

AC=2x+10

AC=2(6)+10

AC=12+10

AC=22

Hope this helped!

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Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4
ivolga24 [154]

Answer:

10.55% probability

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.

1 Bach CD, from a set of 4.

1 Beethoven CD, from a set of 6.

1 Brahms CD, from a set of 3.

1 Handel CD, from a set of 2.

So, D=144

4 CDs from a set of 4+6+3+2 = 15.

So, T= 1365

p= D/T= 144/1365 = 0.1055

10.55% probability that she will choose one by each composer

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3 years ago
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What are two factors to add to give negative 4 and multiply to give negative 10?
SIZIF [17.4K]
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3 years ago
Which of these is not a possible r-value?
Tems11 [23]

Answer:

Step-by-step explanation:

A

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4 years ago
A sector with a radius of 6 cm has a central angle measure of 4pi/9 (in radians). What is the area of the sector?
Usimov [2.4K]

Answer:

The area of the sector is 25.1327 cm²

Step-by-step explanation:

The area of a sector of circunference delimited by an angle in radians can be calculated by using the formula below:

area = (angle*r²)/2

area = [(4*pi/9)*(6)²]/2

area = [(4*pi/9)*36]/2

area = (144*pi/9)/2

area =  144*pi/18

area = 8*pi

area = 25.1327 cm²

The area of the sector is 25.1327 cm²

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3 years ago
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