Provide an appropriate response.The set S of all x that satisfy the inequality ax ? b is a ray in R1. Show that the set S is convex.[Hint: A set S in Rn is convex if, for each p and q in S, the line segment between p and q lies in S. This line segment is the set of points of the form (1 - t)p + tq for 0 ? t ? 1. ]
What will be an ideal response?
Take any p and q in S. Then ap ? b and aq ? b. Take any scalar t such that 0 ? t ? 1. Then 
because (1 - t) and t are both nonnegative and p and q are in S. So the line segment between p and q is in S. Since p and q were any points in S, the set S is convex.
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Solve the problem.Thompson's Hardware spent $15,670 this year on advertising alone. If total sales were $790,100, what percent of total sales was spent on advertising? Round to the nearest tenth of a percent, if necessary.
A. 504% B. 0.2% C. 50.4% D. 2%
Find an equation of a parabola satisfying the given conditions.Focus at (0, -10), directrix y = 10
A. x2 = -10y B. y2 = -40x C. y = -40x2 D. x2 = -40y
Write an equation for the parabola.
A. x2 = 4y B. y2 = -4x C. x2 = -4y D. y2 = 4x
Solve triangle ABC. If necessary, round the answer to the nearest tenth.A = 38.1°, C = 93.1°, b = 16.3 centimeters
A. B = 131.2°, a = 13.4 cm, 
cm
B. B = 131.2°, a = 10.1 cm, 
cm
C. B = 48.8°, a = 13.4 cm, 
cm
D. B = 48.8°, a = 10.1 cm, 
cm