1. a) equation of the line :
y - intercept = -7
so, it will pass through point (0, -7)
and if we plug the value of x as 5, we get
so, it will pass through point (5, -5) too
now, just plot the points (0 , -7) and (5 , -5) and join them.
2. b) equation of line is :
here, y - intercept = 5
so the line passes through point (0 , 5)
now, Plugging the value of x = 1 we get :
so, the given line passes through point (1 , 2)
plotting the points, we can get our required line.
Answer:
- b (x, x - 3, 0)
- d Infinite Solutions
Step-by-step explanation:
1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...
![\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D2%26-2%26-1%266%5C%5C-1%261%263%26-3%5C%5C3%26-3%262%269%5Cend%7Barray%7D%5Cright%5D)
is the matrix ...
![\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%26-1%260%263%5C%5C0%260%261%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%5D)
The first row can be interpreted as the equation ...
x -y = 3
x -3 = y . . . . . add y-3
The second row can be interpreted as the equation ...
z = 0
Then the solution set is ...
(x, y, z) = (x, x -3, 0) . . . . matches selection B
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2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.
2 (x+1) = 3x -1
2x + 2 = 3x - 1
x = -1
Let the original amount be A. Double that would be 2A.
Then, 2A = Ae^(r*5), or 2 = e^(5r).
Taking the natural log of both sides: ln 2 = 5r. Then r = (ln 2)/5 = 0.14
The interest rate would have to be 13.86% per year, written here as r=0.14.
Answer:
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