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olga55 [171]
3 years ago
15

One positive number is 5 times another number . The difference between the two numbers is 80, Find the numbers.

Mathematics
1 answer:
nika2105 [10]3 years ago
4 0
---------------------------------------------------------------------------------------------------
Define the numbers:
---------------------------------------------------------------------------------------------------
Let x be one number.
One number = x
Other number = 5x

---------------------------------------------------------------------------------------------------
Construct the equation:
---------------------------------------------------------------------------------------------------
5x - x  = 80

---------------------------------------------------------------------------------------------------
Combine like terms:
---------------------------------------------------------------------------------------------------
4x = 80

---------------------------------------------------------------------------------------------------
Divide by 4 on both sides:
---------------------------------------------------------------------------------------------------
x = 20

---------------------------------------------------------------------------------------------------
Find the 2 numbers:
---------------------------------------------------------------------------------------------------
One number = x = 20
Other number = 5x = 5(20) = 100

---------------------------------------------------------------------------------------------------
Answer: The two numbers in increasing order are 20 and 100.
---------------------------------------------------------------------------------------------------

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Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

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- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

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- Now we can solve the problem

∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST

- The triangle RST is reflected over the y-axis

- According to the rule above the signs of x-coordinates will change

∵ R = (6 , 6)

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∵ S = (3 , -6)

∴ Its image is (-3 , -6)

∵ T = (0 , 3)

∴ Its image is (0 , 3)

* Now lets look to the figure to find the correct answers

- The image of Δ RST is ΔR'S'T'

∵ The vertices of the image of ΔRST are:

  R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)

* The answer is the second figure

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