Answer:
x < -5 or x = 1 or 2 < x < 3 or x > 3
Step-by-step explanation:
Given <u>rational inequality</u>:





Therefore:

Find the roots by solving f(x) = 0 (set the numerator to zero):



Find the restrictions by solving f(x) = <em>undefined </em>(set the denominator to zero):




Create a sign chart, using closed dots for the <u>roots</u> and open dots for the <u>restrictions</u> (see attached).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Test values: -6, 0, 1.5, 2.5, 4
For each test value, determine if the function is positive or negative:





Record the results on the sign chart for each region (see attached).
As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).
Therefore, the solution set is:
x < -5 or x = 1 or 2 < x < 3 or x > 3
As interval notation:

Step-by-step explanation:
The river is 1000 m wide, and the boat moves at 3 m/s, so the time it takes to cross the river is:
t = (1000 m) / (3 m/s)
t = 333.3 s
The river flows at 2 m/s, so by the time he reaches the other bank, he drifts downstream a distance of:
d = (2 m/s) (333.3 s)
d = 666.7 m
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
Answer:
Representatives of Spain and the United States signed a peace treaty in Paris on December 10, 1898, which established the independence of Cuba, ceded Puerto Rico and Guam to the United States, and allowed the victorious power to purchase the Philippines Islands from Spain for $20 million.