Answer:
a=-6
Step-by-step explanation:
2(3-a)=18
3-a=18/2
3-a=9
a=3-9
a=-6
<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:

Step-by-step explanation:
We are given the following in the question:
Sample size, n = 67
Variance = 3.85
We have to find 80% confidence interval for the population variance of the weights.
Degree of freedom = 67 - 1 = 66
Level of significance = 0.2
Chi square critical value for lower tail =

Chi square critical value for upper tail =

80% confidence interval:

Putting values, we get,

Thus, (3.13,4.91) is the required 80% confidence interval for the population variance of the weights.
Step-by-step explanation:
x + 90⁰ + 90⁰ + 120⁰ = 360 ....sum of angles of quadrilatral is 360⁰
x = 60⁰...
Answer:
The distance of the playground is 540m
Step-by-step explanation:
Here, we are interested in calculating the length of the playground given the information in the question.
Where to attack the question from is the segment that states that he took a break after 480m and also had 2 breaks. Thus, the distance traveled would be 480 * 2 = 960 m
Now, to find the length of the track, we add the distance covered plus the distance uncovered. Mathematically that would be 960m + 120m = 1,080m
In the last part of the question, we are told that the track is twice as long as the playground. This means that the length of the playground or the distance of the playground is 1080/2 = 540 m