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blsea [12.9K]
2 years ago
14

PLEASE ANSWER RIGHT PLEASE

Mathematics
1 answer:
alukav5142 [94]2 years ago
5 0

Answer:

61

Step-by-step explanation:

(x2-x1)2 + (y2-y1)2

(5-0)2 + (-3-3)2

25+36= 61

square root of 61

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Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
Human civilization, at least since the time of ancient Egypt, is on the order of 5000 years old. The age of the Earth is on the
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Write and solve an equation of ratios:

5 *10^9 years       100 m
------------------- = --------------
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Reducing the first fraction,
              
             100 m
10^6 = ----------
                 x
                                100 m
Solving for x,  x = ------------- = 10^(-4) m, or [10^(-1)] * [10^(-3))]
                                10^6
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dexar [7]

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Bailey bought a twin pack of gum for 2 dollars; this is 50 cents less than 2/3 the cost of a triple pack of gum. What is the pri
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Answer:

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Each square on the grid represents 1 yd2.
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The  answer is about 30 yd2 to 40 yd2 or B.


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