Answer:
![x1=\frac{-2-2\sqrt{29401} }{245} x2=\frac{-2+2\sqrt{29401} }{245}](https://tex.z-dn.net/?f=x1%3D%5Cfrac%7B-2-2%5Csqrt%7B29401%7D%20%7D%7B245%7D%20%20x2%3D%5Cfrac%7B-2%2B2%5Csqrt%7B29401%7D%20%7D%7B245%7D)
Step-by-step explanation:
Step One: Convert
49/16x^2-2=-0.05x+4
Step Two: Multiply Both Sides by 80
245x^2-160=-4x+320
Step Three: Move everything to the left
245x^2+4x-480=0
Final Step: Quadratic Formula
![x1=\frac{-2-2\sqrt{29401} }{245} x2=\frac{-2+2\sqrt{29401} }{245}](https://tex.z-dn.net/?f=x1%3D%5Cfrac%7B-2-2%5Csqrt%7B29401%7D%20%7D%7B245%7D%20%20x2%3D%5Cfrac%7B-2%2B2%5Csqrt%7B29401%7D%20%7D%7B245%7D)
Answer:
Step-by-step explanation:
In order to figure out how much money was left in the account after the interest was withdrawn, we have to first find out how much money was initially deposited to earn that amount of interest! The means to find that initial investment is found in the simple interest formula
prt = I, where
p is the initial investement,
r is the interest rate in decimal form,
t is the time in years, and
I is the interest earned. Notice that we have all those things but the p.
Filling in:
p(.0425)(4) = 2380 and
.17p = 2380 so
p = 14000
That means that 14000 was initially invested. If the depositor withdrew the 2380, then
14000 - 2380 is the amount left in the account, namely, $11620
The row echelon form of the matrix is presented as follows;
![\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%200%26%201%20%26%20%20-7%5C%5C%200%260%20%20%261%20%20%5C%5C%5Cend%7Bbmatrix%7D)
<h3>What is the row echelon form of a matrix?</h3>
The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.
The given matrix is presented as follows;
![\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D-3%20%266%20%20%2615%20%20%5C%5C%202%26%20-6%20%26%20%204%5C%5C%201%260%20%20%26-1%20%20%5C%5C%5Cend%7Bbmatrix%7D)
The conditions of a matrix in the row echelon form are as follows;
- There are row having nonzero entries above the zero rows.
- The first nonzero entry in a nonzero row is a one.
- The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.
Dividing Row 1 by -3 gives:
![\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%202%26%20-6%20%26%20%204%5C%5C%201%260%20%20%26-1%20%20%5C%5C%5Cend%7Bbmatrix%7D)
Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;
![\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%200%26%20-2%20%26%20%2014%5C%5C%201%260%20%20%26-1%20%20%5C%5C%5Cend%7Bbmatrix%7D)
Subtracting Row 1 from Row 3 gives;
![\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%200%26%20-2%20%26%20%2014%5C%5C%200%262%20%20%264%20%20%5C%5C%5Cend%7Bbmatrix%7D)
Adding Row 2 to Row 3 gives;
![\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%200%26%20-2%20%26%20%2014%5C%5C%200%260%20%20%2618%20%20%5C%5C%5Cend%7Bbmatrix%7D)
Dividing Row 2 by -2, and Row 3 by 18 gives;
![\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%20%26-2%20%20%26-5%20%20%5C%5C%200%26%201%20%26%20%20-7%5C%5C%200%260%20%20%261%20%20%5C%5C%5Cend%7Bbmatrix%7D)
The above matrix is in the row echelon form
Learn more about the row echelon form here:
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