Answer:
Step-by-step explanation:
Given is a system of equations as
![x1-4x2 - x4 = -7\\ \\x2 - 2x4 = 3 \\\\x4 + 2x5 = 3](https://tex.z-dn.net/?f=x1-4x2%20-%20x4%20%3D%20-7%5C%5C%20%5C%5Cx2%20-%202x4%20%3D%203%20%5C%5C%5C%5Cx4%20%2B%202x5%20%3D%203)
We have 5 variables and 3 equations
a) coefficient matrix of this system is
1 -4 0 -1 0\\
0 1 0 -2 0\\
0 0 0 1 2\\
We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as
1 -4 -1 0\\
0 1 -2 0\\
0 0 1 2\\
b) Augmented matrix is
1 -4 -1 0\\ 7
0 1 -2 0\\
3
0 0 1 2\\3
c) For row operations to ehelon form
we can do R1+4R2 = R1
We get
1 0 -9 0 \\ 19
0 1 -2 0 \\ 3
0 0 1 2 \\ 3
Now let us do R1 = R1+9R3 and R2 = R2+2R3
1 0 0 0 \\ 46
0 1 0 0 \\ 9
0 0 1 2 \\ 3
d) We find that there are infinite solutions to the system in parametric form, since x4 and x5 are linked with only one equation
e) x1 = 46, x2 = 9, x4+2x5 =3
Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution
It's (5,7). This is a translation. (x-4) means moving the x coordinate to the left 4 times. If it was positive it would move to the right. (y+15) moves the y coordinate to the right 15 times also would move to the left if negative.
Your equation will be
15.99x + 12.54y ≤ 125
Hope this helped
Answer:
Slope = 3
Step-by-step explanation:
Calculate using slope formula:
and ![(x2, y2) = (7, 18)](https://tex.z-dn.net/?f=%28x2%2C%20y2%29%20%3D%20%287%2C%2018%29)
![m = \frac{18 - 9}{7 - 4} = \frac{9}{3} = 3](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B18%20-%209%7D%7B7%20-%204%7D%20%3D%20%5Cfrac%7B9%7D%7B3%7D%20%3D%203)
Answer:
The average number of miles is 68.
Step-by-step explanation:
All you need to do with this one is divide the number of miles ridden by the amount of days that it took them. 2,448/36 = 68