Answer:
A. 8π / 3
Step-by-step explanation:
The solution to the system of inequalities is (-3.375, 1.75)
<h3>How to graph the inequalities?</h3>
The system of inequalities is given as:
3y > 2x+12
2x+y < -5
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-3.375, 1.75)
Hence, the solution to the system of inequalities is (-3.375, 1.75)
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Answer: The central angle of the arc is 162 degrees.
Step-by-step explanation: The information available are as follows;
Circumference of the circle equals 10. Length of an arc equals 9/2. The circumference of a circle is given as;
Circumference = 2Pi x r
That means 2Pi x r = 10.
Also the length of an arc along the same circle is 9/2. Length of an arc is calculated as;
Length of arc = (X/360) x 2Pi x r
Where X is the central angle of the arc
That means;
9/2 = (X/360) x 2Pi x r
We can now substitute for the known values as follows
Length of an arc = (X/360) x 2Pi x r
9/2 = (X/360) x 10
9/2 = 10X/360
By cross multiplication we now have
(9 x 360)/(2 x 10) = X
3240/20 = X
162 = X
The angle at the center of the arc is 162 degrees.