The denominator of a fraction is 1 more than 3 times the numerator. If the denominator is doubled and the numerator is increased by 2, the value of the resulting fraction is 1/4. Find the original fraction.
For any arbitrary 2x2 matrices
![\mathbf C](https://tex.z-dn.net/?f=%5Cmathbf%20C)
and
![\mathbf D](https://tex.z-dn.net/?f=%5Cmathbf%20D)
, only one choice of
![\mathbf D](https://tex.z-dn.net/?f=%5Cmathbf%20D)
exists to satisfy
![\mathbf{CD}=\mathbf{DC}](https://tex.z-dn.net/?f=%5Cmathbf%7BCD%7D%3D%5Cmathbf%7BDC%7D)
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on
![\mathbf C](https://tex.z-dn.net/?f=%5Cmathbf%20C)
. One such restriction would be to ensure that
![\mathbf C](https://tex.z-dn.net/?f=%5Cmathbf%20C)
is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking
![\mathbf D=\mathbf C^{-1}](https://tex.z-dn.net/?f=%5Cmathbf%20D%3D%5Cmathbf%20C%5E%7B-1%7D)
we'd get equality.
Answer:
The expressions for the payment made to Mary are,
(Monday) 90 = 15m + b
(Tuesday) 62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.
The equation that represents Mary's earning is
y = 4x + 30
For 20 students,
y = 4(20) + 30 = 110
For Lisa's earnings,
y = 8x + 15
Substituting 20,
y =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.
(Btw this is not my work, I got it from someone else on brainly and wanted to help lol)
Basically, this problem is going to require you to solve for the area and multiply it with the given cost unit.
Area = Length*Height
Area = 100 ft * 8 ft = 800 ft²
Total Cost = (Unit Cost)(Area)
Total Cost = ($2/ft²)(800 ft²)
<em>Total Cost = $1,600</em>
Normally You would need to simplify all of them, to see what their values are like.
Already from the start, however, we can see that 9n + 3 + 2 and 9n + 11 isnt the same value. Based on this, we should only need to simplify one of the other, to get either 9n + 5 or 9n + 11.
Lets pick the upper one.
(4n + 3) + 5n + 8 - 6
4n + 3 +5n + 2
9n + 5.
This indicated that 9n+11 is the odd one.
To make sure, we can solve the next one:
(4n + 5n) + (3 + 8 - 6)
9n + 5
Which indicated the same thing.
9n+11 is the "outsider", which means:
9n + 11 is the correct answer for this task.