Answer:
x=20, 3x=60, 2x=40
Step-by-step explanation:
3x+80+2x=180, so
x=20
Answer:
Step-by-step explanation:
Given is a system of equations as
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
Answer:
A=45
B=110
Step-by-step explanation:
Interior angles of a triangle add up to 180.
So, do 180-25=155.
Then, 155-65=90.
90 divided by 2 is 45.
x=45 so B is 45+65, which is 110.
Answer:
a: 68.08
b: 5.3065
Step-by-step explanation:
The point estimate is a single value. The point estimate for the mean is the mean of the sample. In this case, the mean is the sum of the values divided by the total number of values. The point estimate is the standard deviation of the sample. The standard deviation is the square root of the variance.
See the attached photo for the calculations of these values.