<u>Answer:
</u>
Two required integers are 5 and 10.
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Solution:
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Given that a positive integer is twice another. The sum of the reciprocals of the positive integers is ![\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D)
We have to find the two integers.
Let assume that one integer = x
Since another integer is twice of first one, so second integer = 2x
Reciprocal of first integer = ![\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D)
Reciprocal of first integer = ![\frac{1}{2x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2x%7D)
Given that sum of reciprocal = ![\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D)
![\frac{1}{x}+\frac{1}{2 x}=\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7B2%20x%7D%3D%5Cfrac%7B3%7D%7B10%7D)
On solving above equation for x,
![\frac{2+1}{2 x}=\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B1%7D%7B2%20x%7D%3D%5Cfrac%7B3%7D%7B10%7D)
![\frac{3}{2 x}=\frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%20x%7D%3D%5Cfrac%7B3%7D%7B10%7D)
2x=10
x=5
First integer = x = 5
Second integer = 2x = 10
Hence two required integers are 5 and 10.
Answer:
The answer is 10 blocks.
Step-by-step explanation:
The answer is confusing but you would really ask your self what 5*2 would be because if you were to use blocks you would calculate the length of the route but not the direct distance of home to school.
Answer:
Read below
Step-by-step explanation:
If there are 12 marbles it could split up many different ways for it to be equal among every color. 4 of each for 3 colors or 3 of each for 4 colors. The list goes on you could even have 12 different colors.
Answer:
The equation of the line is: y = x + 4
Step-by-step explanation:
When we are given two points passing through a line, we can find the equation of the line by using two - point form.
Two - point form: ![$ \frac{\textbf{y - y}_\textbf{1}}{\textbf{y}_{\textbf{2}} \textbf{-} \textbf{y}_{\textbf{1}}} = \frac{{\textbf{x - x}_\textbf{1}}}{\textbf{x}_{\textbf{2}} \textbf{-} \textbf{x}_{\textbf{1}} }$](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B%5Ctextbf%7By%20-%20y%7D_%5Ctextbf%7B1%7D%7D%7B%5Ctextbf%7By%7D_%7B%5Ctextbf%7B2%7D%7D%20%5Ctextbf%7B-%7D%20%5Ctextbf%7By%7D_%7B%5Ctextbf%7B1%7D%7D%7D%20%3D%20%5Cfrac%7B%7B%5Ctextbf%7Bx%20-%20x%7D_%5Ctextbf%7B1%7D%7D%7D%7B%5Ctextbf%7Bx%7D_%7B%5Ctextbf%7B2%7D%7D%20%5Ctextbf%7B-%7D%20%5Ctextbf%7Bx%7D_%7B%5Ctextbf%7B1%7D%7D%20%20%20%20%7D%24)
where
are the points passing through the line.
Here, let us take two points (can be any two):
and
![$ (x_2, y_2) = (5, 9) $](https://tex.z-dn.net/?f=%24%20%28x_2%2C%20y_2%29%20%3D%20%285%2C%209%29%20%24)
Therefore, we have:
![$ \frac{y - 5}{9 - 5} = \frac{x - 1}{5 - 1} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7By%20-%205%7D%7B9%20-%205%7D%20%3D%20%5Cfrac%7Bx%20-%201%7D%7B5%20-%201%7D%20%24)
![$ \iff \frac{y - 5}{4} = \frac{x - 1}{4} $](https://tex.z-dn.net/?f=%24%20%5Ciff%20%5Cfrac%7By%20-%205%7D%7B4%7D%20%3D%20%5Cfrac%7Bx%20-%201%7D%7B4%7D%20%24)
![$ \iff y - 5 = x - 1 $](https://tex.z-dn.net/?f=%24%20%5Ciff%20y%20-%205%20%3D%20x%20-%201%20%24)
![$ \implies y = x - 1 + 5 $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20y%20%3D%20x%20-%201%20%2B%205%20%24)
which is the required answer.