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diamong [38]
3 years ago
9

Angles ABC and DBE are vertical angles, with angle ABC = 4x, and angle DBE =( 2x+18)

Mathematics
1 answer:
Dmitrij [34]3 years ago
3 0
 V<span>ertical angles are equal.
We have 4x = 2x + 18.
Then, 2x = 18;
x = 18 </span>÷ 2;
x = 9 degrees;
The measure of angle DBE is 2 × 9 + 18 = 36 degrees.
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Answer:

<em>Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.</em>

Step-by-step explanation:

Pratap Puri rowed 10 miles down a river in 2 ​hours, but the return trip took him 2.5 hours.

We know that, Speed = \frac{Distance}{Time}

So, the <u>speed of Pratap with the current</u> will be:  (\frac{10}{2})miles/hour = 5 miles/hour

and the <u>speed of Pratap against the current</u> will be:  (\frac{10}{2.5})miles/hour = 4 miles/hour.

Suppose, the rate of Pratap in still water is x and the rate of current is y.

So, the equations will be........

x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)

Adding equation (1) and (2) , we will get......

2x=9\\ \\ x=\frac{9}{2}= 4.5

Now, plugging this x=4.5 into equation (1), we will get.....

4.5+y=5\\ \\ y=5-4.5 =0.5

Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.

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