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Evgen [1.6K]
3 years ago
10

Rationalize the denominator.

Mathematics
1 answer:
mel-nik [20]3 years ago
3 0

Answer:

7sqrt(15) - 5sqrt(6)

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

45

Step-by-step explanation:

7 -sqrt(10)

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

3 sqrt(5) *sqrt(3)

7 -sqrt(10)

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

3 sqrt(15)

Multiply the top and bottom by sqrt(15)/ sqrt(15)

7 -sqrt(10)               sqrt(15)

----------------------- * ------------

3 sqrt(15)                 sqrt(15)


(7 -sqrt(10))* sqrt(15)

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

3 *15

Distribute


7sqrt(15) - sqrt(150)

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

45

sqrt(ab) =sqrt(a) sqrt(b)

150 = 25*6

7sqrt(15) - sqrt(25)sqrt(6)

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

45

7sqrt(15) - 5sqrt(6)

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

45

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3 years ago
A scale on a map shows that 2 inches = 25 miles.
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To find the answer, cross multiply 2/25 with x/60
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dori left her house at 12:00 pm and walked at 50 steps per minute and malory left her house at 12:20 and walked 90 steps per min
JulijaS [17]

Answer:

Malory will catch up with Dori in 25 minutes.

Step-by-step explanation:

Given:-

Dori walking at 50 steps/min.

Malory walking at 90 steps/min.

Now, as Dori left the house 20 mins  ahead of Malory and

Dori is walking at speed of 50 steps/min, that means

Dori is walking ahead of Malory by 50 (steps) \times 20 (minutes)

Dori is walking ahead of Malory by 50\times 20

Dori is walking ahead of Malory by = 1000 steps

Now, let time be t of walking by Dori and Malory,

to calculate the time for Malory to catch up with Dori can be written as,

(50\times t)+1000=90\times t

where, 1000 is the headstart for Dori, 50 and 90 is the walking speed of Dori and Malory respectively in steps/ min.

90t-50t=1000

40t=1000

t=\frac{1000}{40}

t=25\ minutes

Therefore Malory will catch up with Dori in 25 minutes.

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