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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:
Equation: 
Solution: 
Step-by-step explanation:
Let be "t" the number of movie tickets bought by the group of friends.
According to the information given in the exercise, the price of each movie ticket is: $8.50.
Then, you can represent the amount (in dollars) the group of friends spent in movie tickets, with this expression:
You know that one person spent $6.50, then the expression that represents the total amount (in dollars) the group of friends spent in food and movie tickets, is:
Since that total amount spent is given in the exercise, you can write the following equation to determine how many tickets were bought:
Finally, you can solve for "t" in order to find the solution of the equation. This is:
Derek would have planted the tree 7 years ago. You subtract 36 from 44.75 and get 8.75. This is how much the tree grew since he planted it. Then, you'll divide 8.75 by 1.25 (1 1/4) which tells you how many years it has been since he planted the tree. The final answer is 7 years. Hope this helps!
Answer : (0,3) U (3, ∞)
We need to find the interval(s) over which the function is decreasing
We look at the intervals of x where the graph is decreasing
Decreasing interval of the graph is the part where the graph goes down
We look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph changes direction and start decreasing at x=0
the graph is decreasing till x=3
so first decreasing interval is x=0 to 3. we write it as (0,3)
After x=3 the graph starts decreasing and it goes to infinity
So the second decreasing interval is 3 to infinity . We write it as (3, ∞)
Now combine both intervals by a 'U' union
(0,3) U (3, ∞)
Answer:
X=7/2
x=3.5
Step-by-step explanation:
Hope this helped you.. Have a nice day dear...❤️
