number of pockets inside jacket
Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
The answer would be D. When it comes to home loans, having a
good payment record and a decent job history is important. It is in this way
that lenders are going to have the assurance they need with regards to being paid
back on time with the money they lent.
For this case we must find the solution of the following quadratic equation:
![x ^ 2 + 5x + 7 = 0](https://tex.z-dn.net/?f=x%20%5E%202%20%2B%205x%20%2B%207%20%3D%200)
Where:
![a = 1\\b = 5\\c = 7](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%205%5C%5Cc%20%3D%207)
Then, the solution is given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Substituting the values:
![x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-5%20%5Cpm%20%5Csqrt%20%7B5%20%5E%202-4%20%281%29%20%287%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-5%20%5Cpm%20%5Csqrt%20%7B25-28%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-5%20%5Cpm%20%5Csqrt%20%7B-3%7D%7D%20%7B2%7D)
By definition we have:![i ^ 2 = -1](https://tex.z-dn.net/?f=i%20%5E%202%20%3D%20-1)
![x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-5%20%5Cpm%20%5Csqrt%20%7B3i%20%5E%202%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-5%20%5Cpm%20i%20%5Csqrt%20%7B3%7D%7D%20%7B2%7D)
Thus, we have two complex roots.
Answer:
The equation has no real roots.