Answer:
x = -10
Step-by-step explanation:
3(x+1) +5 = 2x -2
<em>Distribute the 3 to the x+1</em>
3x+3 +5 = 2x -2
<em>Combine like terms</em>
3x + 8 = 2x -2
<em>Subtract 2x from both sides</em>
x + 8 = -2
<em>Subtract 8 from both sides</em>
x = -10
Hope this helps!
The bathtub will hold 74.375 ft^3 (or cubic feet) of water. To find the volume of the rectangular prism shape, use the formula v=lwh, which means volume=length*width*height; where * is the symbol for multiplication.
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This is the formula for circumference of circle
Answer : value of x and y in the matrix equation is:
x = -3
y = +4, -4
Step-by-step explanation :
The matrix expression is:
![\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B4%5C%5Cy%5E2%2B1%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-9x%5C%5C-17%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D28%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
First we have to add left hand side matrix.
![\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28x%2B4%29%2B%28-9x%29%5C%5C%28y%5E2%2B1%29%2B%28-17%29%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D28%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Now we have to add left hand side terms.
![\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B4-9x%5C%5Cy%5E2%2B1-17%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D28%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-8x%5C%5Cy%5E2-16%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D28%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Now we have to equating left hand side matrix to right hand matrix, we get:
Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.
<span>Don't forget S is measured in thousands of units so you are solving for :
100 < 74.5 + 43.75Sin(πt/6)
25.5 < 43.75Sin(πt/6)
Sin(πt/6) >25.5/43.75 = 0.582857
ASrcSin(πt/6) > 0.62224 radians
πt/6 > 0.62224
t > 6 x 0.62224/π = 1.1884 (4dp)
This initial value occurs when the sine value is increasing and it will reach its maximum value of 1 when Sin(πt/6) = Sinπ/2, that is when t = 3.
Consequently, monthly sales exceed 100,000 during the period between t = 1.1884 and 4.8116
[3 - 1.1884 = 1.8116 so the other extreme occurs at 3 + 1.8116]
Note : on the basis of these calculations, January is 0 ≤ t < 1 : February is 1 ≤ t < 2 :....May is 4 ≤ t < 5
So the period when sales exceed 100,000 occurs between Feb 6 and May 25 and annually thereafter.</span>
