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3 years ago

In the figure above AB = 4x + 6 and BC = 7x + 15. If AC = 120, find the length of segment AB.

Mathematics

1 answer:

Mrac [35]3 years ago

7 0

Answer:

x = 9

Step-by-step explanation:

AB = 4x + 6 and BC = 7x + 15 AC is the sum of AB and BC

so 4x + 6 + 7x + 15 = 120 add like terms

11x + 21 = 120 subtract 21 from both sides

11x = 99 divide both sides by 11

x = 9

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3 years ago

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4 years ago

There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - W

jenyasd209 [6]

Answer:

Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old.

Step-by-step explanation:

Let $k$ be Kirk's age.

Let $b$ be Brian's age.

Let $m$ be Matt's age.

Let $m_{1}$ be the boss/manager's age.

From the information given, we can set up 4 equations:

$k+b+m+m_{1}=106$

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$b=2m_{1}-12$

$m=\frac{1}{2}m_{1}+6$

Rewrite the first equation, substituting $k$ , $b$ , and $m$ in terms of $m_{1}$ to get:

$2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106$

Open up the parentheses using the distributive property (which is $a(b-c)=ab-ac$ ) and combine like terms to get:

$5.5m_{1}-26=106$

Add 26 to both sides to reach:

$5.5m_{1}=132$

Thus, $m_{1}=24$ . Substitute $24$ for $m_{1}$ in the second, third, and fourth original equations to find that $k=28$ , $b=36$ , and $m=18$ . Therefore, Kirk is 28 years old, Brian is 36 years old, Matt is 18 years old, and the manager is 24 years old. To check, you can add up all of the ages to get 106.

Hope this helps :)

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3 years ago