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Pavel [41]
2 years ago
9

What is the range of AB?

Mathematics
1 answer:
lana66690 [7]2 years ago
3 0

a, b, c - sides of a triangle

Therefore:

a + b > c

a + c > b

b + c > a

---------------------------------

We have a = AB, b = 140mi, c = 100mi.

(1)     a + b > c

AB + 140 > 100    <em>subtract 140 from both sides</em>

AB > -40 → AB > 0

----------

(2)    a + c  > b

AB + 100 > 140      <em>subtract 100 from both sides</em>

AB > 40

-----------

(3)    b + c > a → a < b + c

AB < 140 + 100

AB < 240

<h3>Answer: 40 < AB < 240</h3>
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Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura
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Answer:

17 miles.

Step-by-step explanation:

Let's define:

North as the positive y-axis

East as the positive x-axis.

We know that Laura lives 15 miles east of Kevin's place.

Kevin lives 8 miles south of Michelle's place.

So, if we define the origin, (0, 0) as Laura's place.

From:

"that Laura lives 15 miles east of Kevin's place."

We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:

(0, 0) + (-15mi, 0) = (-15mi, 0)

From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.

Then the location of Michele's house is the location of Kevin's plus (0, 8mi).

Michelle's house is located at:

(-15mi, 0) + (0, 8mi)  =(-15mi, 8mi)

Now we want to find the distance between Michelle's house and Laura's house.

Michelle's house is at (-15mi, 8mi)

Laura's house is at (0mi, 0mi)

Remember that the distance between two points (a, b) and (c, d) is given by:

D = \sqrt{(a - c)^2 + (b - d)^2}

Then the distance between  (-15mi, 8mi) and (0mi, 0mi) is:

D = \sqrt{(-15mi - 0mi)^2 + (8mi - 0mi)^2} = 17mi

The correct option is the first one, 17 miles.

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Answer:


Step-by-step explanation:

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