The two numbers are -6 and -20
-20 x -6 = 120
-20 + (-6) = -26
The average speed of the runner is 12.7 mph and 20.4 km/h
Given that the runner ran 26.2 mile in 2hr and 4 minutes, we start of by converting the time from hours and minutes into minutes and finally hours, since hours is what we need. So, we have
2hr = 120mins
+ 4 mins = 124 mins
124 mins ÷ 60 hour/mins = 2.06 hours.
This means that the runner finished the race in 2.06 hours.
If we are to find the average speed in mile per hour, we have
Average speed = distance ran ÷ time taken
Average speed = 26.2 ÷ 2.06
Average speed = 12.7 mph
From the speed in mph, we can directly convert it to km/hr by saying
1 mph = 1.609 km/h
12.7 mph = 12.7 * 1.609 = 20.4 km/hr
for more, check: brainly.com/question/1989219
20 = 40e^-0.1446t
e^-0.1446t = 0.5
t = ln 0.5 / -0.1446
t = 4.8 days
Answer:
Infinite number of solutions.
Step-by-step explanation:
We are given system of equations
Firs we find determinant of system of equations
Let a matrix A=![\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%264%265%5C%5C1%261%262%5C%5C2%261%26-1%5Cend%7Barray%7D%5Cright%5D)
and B=![\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5C%5C1%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.
We are finding rank of matrix
Apply 
and 
![\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C1%261%262%5C%5C0%26-1%26-3%5Cend%7Barray%7D%5Cright%5D)
:![\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C1%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
Apply
![\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C0%261%261%5C%5C0%26-1%26-3%5Cend%7Barray%7D%5Cright%5D)
:![\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C6%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
Apply 
![\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C0%261%261%5C%5C0%260%26-2%5Cend%7Barray%7D%5Cright%5D)
:![\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C6%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Apply 
and 
![\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
:![\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C%5Cfrac%7B13%7D%7B2%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Apply 
![\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
:![\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B9%7D%7B2%7D%5C%5C%5Cfrac%7B13%7D%7B2%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.
Therefore, rank of matrix is equal to rank of B.
Answer:
(x - 3)(x + 1)(x + 5)
Step-by-step explanation:
I'd use synthetic division instead. If we were to find the roots of the given polynomial, we could from them write the factors as well.
The divisor x + 5 corresponds to root x = -5. Setting up synthetic div.,
-5 ) 1 3 -13 -15
-5 10 +15
-----------------------------
1 -2 -3 0
Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor. Moreover, we know that the coefficients of the quotient are 1, -2 and -3.
1x² - 2x - 3 can be factored: the factors are (x - 3) and (x + 1).
So the end result for this problem is (x - 3)(x + 1)(x + 5).
