Step-by-step explanation:
2x = y-10
Rewrite as: 2x + 10 = y
Therefore:
2x+10 = y
2x +7 = 2y
Subtract the equations:
2x + 10 = y
- 2x + 7 = 2y
______________
3 = -y
Therefore y = -3
Substiture y = -3 into the second equation:
2x + 7 = 2(-3)
2x + 7 = -6
2x = -13
x= -6.5
Answer : (-6.5, -3)
Answer:
The Pythagorean identity states that
![\sin^2 t + \cos^2 t = 1](https://tex.z-dn.net/?f=%5Csin%5E2%20t%20%2B%20%5Ccos%5E2%20t%20%3D%201)
Using that we can rewrite the left denominator as:
![1 - \sin^2 t](https://tex.z-dn.net/?f=1%20-%20%5Csin%5E2%20t)
Which can be factored as
![(1 - \sin t)(1+ \sin t)](https://tex.z-dn.net/?f=%281%20-%20%5Csin%20t%29%281%2B%20%5Csin%20t%29)
The numerator we can expand as:
![(1 - \sin t)(1 - \sin t)](https://tex.z-dn.net/?f=%281%20-%20%5Csin%20t%29%281%20-%20%5Csin%20t%29)
On the right hand side, let's multply numerator and denominator with (1 - sin t):
The total formula then becomes:
![\dfrac{(1-\sin t)(1-\sin t)}{(1 - \sin t)(1 + \sin t)} = \dfrac{(1-\sin t)(1 - \sin t)}{(1+\sin t)(1 - \sin t)}](https://tex.z-dn.net/?f=%5Cdfrac%7B%281-%5Csin%20t%29%281-%5Csin%20t%29%7D%7B%281%20-%20%5Csin%20t%29%281%20%2B%20%5Csin%20t%29%7D%20%3D%20%5Cdfrac%7B%281-%5Csin%20t%29%281%20-%20%5Csin%20t%29%7D%7B%281%2B%5Csin%20t%29%281%20-%20%5Csin%20t%29%7D)
There you go... left and right are equal.
Answer:
Therefore values of a and b are
![a=3\ and\ b = 2](https://tex.z-dn.net/?f=a%3D3%5C%20and%5C%20b%20%3D%202)
Step-by-step explanation:
Rewrite
in the form
where a and b are integers,
To Find:
a = ?
b = ?
Solution:
..............Given
Which can be written as
![(\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%20coefficient%5C%20of%5C%20x%29%5E%7B2%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-6%29%5E%7B2%7D%3D9)
Adding half coefficient of X square on both the side we get
...................( 1 )
By identity we have (A - B)² =A² - 2AB + B²
Therefore,
![x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D-6x%2B9%3Dx%5E%7B2%7D-2%5Ctimes%203%5Ctimes%20x%2B3%5E%7B2%7D%3D%28x-3%29%5E%7B2%7D)
Substituting in equation 1 we get
![(x-3)^{2}=2](https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%3D2)
Which is in the form of
![(x-a)^{2}=b](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%3Db)
On comparing we get
a = 3 and b = 2
Therefore values of a and b are
![a=3\ and\ b = 2](https://tex.z-dn.net/?f=a%3D3%5C%20and%5C%20b%20%3D%202)
Answer:
6 days
Step-by-step explanation
2/3 cups x 3 days = 2 cups
2 cups x 2 cups = 4 cups
4 cups = 6 days
Answer:
u r correct
look at the picture I sent