Answer:
Step-by-step explanation:
From the figure attached,
If the figures shown are congruent (Equal in shape and size), length of all the sides must be equal.
Therefore, sides sides CD and GH must be equal in measures.
Distance between the two points and is given by,
d =
Length of the side CD having ends C(-4, 4) and D(0, 5) will be,
CD =
CD =
=
Length of GH having ends G(0, -4) and H(4, -5) will be,
GH =
=
=
Therefore, m(CD) = m(GH)
Similarly, we can prove all corresponding sides of two figures equal in measure.
This shows ABCD ≅ EFGH.
Vertical angles are congruent (equal), and the angles below are vertical angles.
x + 40 = 3x
40 = 3x - x
2x = 40
<u><em>x = 20</em></u>
Answer:
Area (A) = ½ (b × h) square units
Step-by-step explanation:
The general formula for calculating the area of a triangle is; Area (A) = ½ (b × h) square units, where; A is the area, b is the base, and h is the triangle's height. The triangles might be different in nature, but it important to note that this formula applies to all the triangles.
Answer:
The probability of the system being down in the next hour of operation is 0.3.
Step-by-step explanation:
We have a transition matrix from one period to the next (one hour) that can be written as:
We can represent the state that system is initially running with the vector:
The probabilties of the states in the next period can be calculated using the matrix product of the actual state and the transition matrix:
That is:
With the inital state as running, we have a probabilty of 0.7 that the system will be running in the next hour and a probability of 0.3 that it will be down.