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frutty [35]
4 years ago
8

Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain​

Mathematics
1 answer:
Darina [25.2K]4 years ago
6 0

√(<em>x</em> + 1) + 3 = 0   ==>   √(<em>x</em> + 1) = -3

has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives

(√(<em>x</em> + 1))² = (-3)²   ==>   <em>x</em> + 1 = 9   ==>   <em>x</em> = 8

But this is not a valid solution, since

√(8 + 1) = √9 = 3 ≠ -3

While -3 is a square root of 9, we had started off with the *positive* square root of <em>x</em> + 1.

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A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still w
prohojiy [21]

Step-by-step explanation:

Given that,

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,

We know that,

Speed = distance/time

The rate while moving downstream=\dfrac{60}{3}=20\ mph

The rate while moving upstream =\dfrac{60}{5}=12\ mph

The rate of the boat in still water is the average of these:

v_s=\dfrac{20+12}{2}=16\ mph

The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph

Hence, this is the required solution.

7 0
3 years ago
here were 84 runners to start a race. in the first half of the race, 13 of them dropped out. in the second half of the race, 14
Gala2k [10]
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8 0
4 years ago
The actual distance from Pittsburgh, PA to Philadelphia PA is 304 miles. On a map the distance is 14 inches. Complete the scale
katrin2010 [14]
1 inch = 21.7 miles
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5 0
3 years ago
Read 2 more answers
Use the approach in Gauss's problem to find the sums of the arithmetic sequences below
I am Lyosha [343]

Answer:

15150 is the required sum.

Step-by-step explanation:

Gauss method of summing sequences like this is to add the first term to the last term, the second term to the second to the last term and so on until you get to the middle. By doing this, you will always get the same sum. Then you divide the number of terms by two, because you are technically adding the first half of the sequence to the second half. You then multiply the sum of each pair that gave the same number with the number of terms that has been divided by 2. For this problem we have:

3 + 300 = 303

6 + 297 = 303

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and so on.

100÷ 2 = 50.

Therefore we have 50 * 303 = 15150 is the required sum.

5 0
3 years ago
Anyoneee?? Mean Median and mode
juin [17]

Answer:

mode is the most occuring number which is in this case 11

you get the median by putting them in order from least to greatest and them marking them out until you get to the middle but if there are two numbers in the middle you add them and then divide by two and that is your median but in this case your median is 11

you get the mean by adding all the numbers together and dividing by how many numbers there are so in this case you are dividing by 9 and when you add oall of these numbers together you get 98 and 98/9 is 10.8888888889 which you would round and get 10.9

hope this helps

3 0
3 years ago
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