Answer:
Step-by-step explanation:
Simplify the numerator:
Rewrite 4 as
Rewrite as
Since both terms are perfect squares, factor using the difference of squares formula, and b = 5x.
Multiply 5 by -1.
Simplify the denominator:
Subtract x from -11x
Factor 2x out of
Answer:
Option C.
Step-by-step explanation:
we have
-----> equation A
-----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
using a graphing tool
see the attached figure
The intersection point is (3,-7) -----> is a common point both lines
The point (1,-3) belong to the line A
The point (6,-6) belong to the line B
therefore
a line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6
Assuming the equation is x^2 + y^2 = 1, then that's a circle, with radius 1, centered on the origin [0,0].
So there are two tangents at x = 0. They are y = 1, and y = -1 (horizontal lines).
There is one tangent at x = 1. It is x = 1 (a vertical line).
There is no tangent at x = 35, because the original equation has no solution at x = 35.
Answer:
i) True
ii) True
Step-by-step explanation:
<u>Given :-</u>
Point (-1, 2)
<u>To Find :</u>
Whether the point is a solution of :
- y = -2x
- y = x + 3
<u>Solving :-</u>
Substitute the value of the point in each of the equations.
=> y = -2x
=> 2 = -2(-1)
=> 2 = 2 [∴ The point makes it true]
=> y = x + 3
=> 2 = -1 + 3
=> 2 = 2 [∴ The point makes it true]
Answer:
a. 1.92 customer
b. 400 seconds.
c. 0.6944
Step-by-step explanation:
The system described is a waiting line type (M / M / 1) with 100s service time, that is, a service rate mu = 36 customers / hour; and a lambda arrival rate = 25 customers / hour. In this way,
a. The number of customers waiting to use the machine is: lambda ^ 2 / [mu (mu - lambda)] = (25^2) / [36 (36 - 25)] = (25^2) / (36*9) = 1.92 customers .
b. The average time a client spends in the system is: 1 / (mu - lambda) = 1 / (36 - 25) = 1/9 = 0.11 hours = 400 seconds.
c. The probability that a arriving customer should wait for the service is given by: lambda / mu = 25/36 = 0.6944.