3 miles each day for x days is 3x
5 miles each day for y days is 5y
Frank ran at least as many miles as Latoya is 3x >/= 5y
Answer:
Therefore, the inverse of given matrix is

Step-by-step explanation:
The inverse of a square matrix
is
such that
where I is the identity matrix.
Consider, ![A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%263%5C%5C3%266%5Cend%7Barray%7D%5Cright%5D)








Therefore, the inverse of given matrix is

A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
Options
(A) (9,0) (B) (-2,20) (C) (-5,2) (D) (0,-9)
Answer:
(B) (-2,20)
Step-by-step explanation:
Given the objective function, C=3x-4y
The vertex at which C is minimized will be the point (x,y) at which the expression gives the lowest value.
<u>Option A </u>
At (9,0), x=9, y=0
C=3(9)-4(0)=27-0
C=27
<u>Option B </u>
At (-2,20), x=-2, y=20
C=3(-2)-4(20)=-6-80
C=-86
<u>Option C</u>
At (-5,2), x=-5, y=2
C=3(-5)-4(2)=-15-8
C=-23
<u>Option D </u>
At (0,-9), x=0, y=-9
C=3(0)-4(-9)=0+36
C=36
The lowest value of C is -86. This occurs at the vertex (-2,20).
Therefore, the objective function C=3x-4y is minimized at (-2,20).