<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:
3
Step-by-step explanation:
j(2) means that x equals 2...
the first inequality in the function says that x is greater than or equal to 2
the second inequality states that x is greater than 2(not equal to) and is less than or equal to 5
the third one states that x is greater than 5
x applies to the first inequality since we know that x can be equal to 2
Now, to the number before the if
there is a 3 before the if in the first inequality
This means that if x is greater than or equal to 2 the y or the function would equal 3
therefore, j(2) would equal 3
I hope this helps!!!
<h3>
Answer: n - 10 which is choice C</h3>
Let's use an example. If Nathaniel earned $15 on Tuesday, and earned $10 less on Wednesday, then 15-10 = 5 dollars is the amount he earns on Wednesday.
Now let's say he earned $27 on Tuesday, and still earned $10 less the next day, meaning that he earns 27-10 = 17
Whatever he earns on Tuesday, subtract off 10. That's the rule to follow for this problem.
(amount earned on Tuesday) - 10 = amount earned on Wednesday
If n reprsesent the placeholder for "amount earned on Tuesday", then we can rewrite that equation as
amount earned on Wednesday = n - 10
In short, whatever 'n' is, subtract 10 off it. In the examples above, I used n = 15 and n = 27.
note: the order of subtraction matters. The expression n-10 is not the same as 10 - n. If you subtract in the wrong order you may get a negative value (eg: 10 - 17 = -7), but he can't earn a negative amount of dollars.
No an obtuse angle does not have a complement
