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Umnica [9.8K]
3 years ago
6

The sum of the reciprocals of two consecutive integers is 9/20. Determine the consecutive integers algebraically.

Mathematics
2 answers:
fredd [130]3 years ago
8 0

Answer : The two consecutive integers are, 4 and 5

Step-by-step explanation :

Let the two consecutive number be, x and (x+1)

The sum of the reciprocals of two consecutive integers is 9/20.

The expression will be:

\frac{1}{x}+\frac{1}{x+1}=\frac{9}{20}

Now solving the term 'x', we get:

\frac{x+1+x}{(x)(x+1)}=\frac{9}{20}

\frac{2x+1}{x^2+x}=\frac{9}{20}

20(2x+1)=9(x^2+x)

40x+20=9x^2+9x

9x^2-31x-20=0

We are solving the quadratic equation by middle term splitting.

9x^2-36x-5x-20=0

9x(x-4)+5(x-4)=0

(9x+5)(x-4)=0

(9x+5)=0\text{ and }(x-4)=0

x=\frac{-5}{9}\text{ and }x=4

We are neglecting the value of x=\frac{-5}{9}

Thus we are taking x = 4

When x = 4 then (x+1) = (4+1) = 5

Thus, the two consecutive integers are, 4 and 5

DochEvi [55]3 years ago
3 0
The answer is 2 1/5.
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How do I find the percentile of someone with a certain number of things from a dot plot data set?
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3 years ago
Two towns that are 31.5 km apart are 3 cm apart on a map. what is the scale of the map?
VLD [36.1K]

<u>Answer:</u>

1 cm : 10.5 km

<u>Step-by-step explanation:</u>

We are given that two towns are 31.5 km in real and are 3 cm apart on a map and we are to find the scale of the map.

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Answer:

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Step-by-step explanation:

First draw a rectangle and draw a diagonal line in the middle. The line makes two triangles, and the line itself is the hypotenuse. So, to find hypotenuse, the formula is:

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