Answer:
The solution to the equation system given is:
- <u>x = 2</u>
- <u>y = -1</u>
Step-by-step explanation:
First, we must know the equations given:
- 2x + 3y = 1
- 3x + y = 5
Following Crammer's Rule, we have the matrix form:
![\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Now we solve using the determinants:
![x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%281%2A1%29-%285%2A3%29%7D%7B%282%2A1%29-%283%2A3%29%7D%20%3D%20%5Cfrac%7B1-15%7D%7B2-9%7D%20%3D%5Cfrac%7B-14%7D%7B-7%7D%20%3D%202)
![y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%282%2A5%29-%283%2A1%29%7D%7B%282%2A1%29-%283%2A3%29%7D%3D%5Cfrac%7B10-3%7D%7B2-9%7D%20%3D%5Cfrac%7B7%7D%7B-7%7D%3D-1)
Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:
- 2x + 3y = 1
- 2(2) + 3(-1)= 1
- 4 - 3 = 1
- 1 = 1
And, with the second equation:
- 3x + y = 5
- 3(2) + (-1) = 5
- 6 - 1 = 5
- 5 = 5
Answer:
angle 6 is 30 degrees
Step-by-step explanation:
its because 180/6 = 30
and 30 x 5 = 150 and 150 + 30 =180
hope this helps
Answer:
x = -4
Step-by-step explanation:
Solve for x:
3 x - 5 x + 2 = 10
Grouping like terms, 3 x - 5 x + 2 = 2 + (3 x - 5 x):
2 + (3 x - 5 x) = 10
3 x - 5 x = -2 x:
-2 x + 2 = 10
Subtract 2 from both sides:
(2 - 2) - 2 x = 10 - 2
2 - 2 = 0:
-2 x = 10 - 2
10 - 2 = 8:
-2 x = 8
Divide both sides of -2 x = 8 by -2:
(-2 x)/(-2) = 8/(-2)
(-2)/(-2) = 1:
x = 8/(-2)
The gcd of 8 and -2 is 2, so 8/(-2) = (2×4)/(2 (-1)) = 2/2×4/(-1) = 4/(-1):
x = 4/(-1)
Multiply numerator and denominator of 4/(-1) by -1:
Answer: x = -4
Answer: If the level of confidence is increased without changing the sample size then<em> </em><u><em>The margin of error will decrease because the critical value will decrease. The decreased margin of error will cause the confidence interval to be narrower.</em></u>
where;
<em>Margin of error = Critical value × Standard deviation</em>
<em>Here, it can be duly noted that Margin of error has a positive relation with critical value, i.e </em><u><em>The margin of error will decrease because the critical value will decrease.</em></u>
<u><em>whereas;</em></u>
The confidence interval is <em>the value ± the margin of error.</em>
<em>Therefore, </em><u><em>the decreased margin of error will cause the confidence interval to be narrower.</em></u>
Answer:
285 = 50h + 60; 4.5 hours
Step-by-step explanation:
$50 per hour - 50h
$60 for parts - 60
$285 total
285 = 50h + 60
225 = 50h
h = 4.5
The plumber worked for 4.5 hours to fix the leaky sink