p(x) and q(x) have different domains and different ranges
Answer:
Darius is correct if only the median score is considered.
Step-by-step explanation:
Darius scores are; 96, 54,120, 87, 123
arrange the scores in increasing order;
54,87,96,120,123
mean = (54+87+96+120+123)/5 =480/5 =96
median =96
Barb's scores are 92,94,96,98,110
mean=(92,94,96,98,110)/5 =490/5=98
median score=96
⇒if the median score only is considered; then it is a tie because the score is 96 in both players.
Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
