<h3>
Answer: x = 7 and y = 3</h3>
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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
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Let's consider case A
We have this system of equations

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
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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.
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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.
Answer:
10.12
Step-by-step explanation:
Given:
- 0.07 cm thick = 0.007m and it is dr (the change in radius)
As we know that, the volume of a hemispherical dome with diameter 48 m is:
- V =
π
Take the derivative of V we have:
= 2π
<=> dV = 2π
*dr
<=> dV = 2π*
*0.0007 = 10.12
Hope it will find you well.
The point (5, 3) is in first quadrant, then after the 90° clockwise the point will be in fourth quadrant and the coordinate will get swap. Then the coordinate will be (3, -5).
<h3>What is a transformation of a point?</h3>
A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
If the point A at (5, 3) is rotated clockwise about the origin through 90°.
Then the coordinates of the new point will be
The point (5, 3) is in first quadrant, then after the 90° clockwise the point will be in fourth quadrant and the coordinate will get swap.
Then the coordinate will be (3, -5).
More about the transformation of a point link is given below.
brainly.com/question/27224339
#SPJ1
Answer:
$0.50
Step-by-step explanation:
multiply 3.50 by 7 and you get 24.5. $25.00-$24.50= $0.50