Answer:
11. O = (-1, 5/2); 12. H = (1,4)
Step-by-step explanation:
11. Circumcentre
Your points form the vertices of a right triangle (see image below).
The circumcentre (O) of a right triangle must be at the midpoint of the hypotenuse.
Your hypotenuse has the ends at (-3,4) and (1,1), so
O = ((-3 + 1)/2),(4 + 1)/2))
O = (-2/2,5/2)
O = (-1, 5/2)
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12. Orthocentre
The orthocentre (H) of a right triangle is the vertex at the right angle.
Your right angle is at (1, 4), so
H= (1,4)
The piecewise function describing the cost C of the reunion are C(x) = 500 + 17.5x, where x <= 40 and C(x) = 1200 + 14.75(x - 40), where x > 40
<h3>Write a piecewise function describing the cost C of the reunion.</h3>The given parameters are:
Reserve = $500
Cost per guest = $17.50 for the first 40 guests
Cost per guest = $14.75 for each additional guest
The above means that
C(x) = 500 + 17.5x, where x <= 40
C(x) = 500 + 17.5 * 40 + 14.75(x - 40), where x > 40
Next, we evaluate the functions
This gives
C(x) = 500 + 17.5x, where x <= 40
C(x) = 1200 + 14.75(x - 40), where x > 40
<h3>Use a graphing calculator to graph the function</h3>To do this, we simply plot each function with its domain
See attachment for the graph of the piecewise functions
Read more about piecewise functions at
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