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Anarel [89]
3 years ago
15

A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour l

onger than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
Mathematics
1 answer:
LiRa [457]3 years ago
5 0
You need to write the equation out as you read it. D*(1/50) + D*(1/40) = 2D*(1/45) + 1/2. Solve for D
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P(x)=3x^2+12x+7 find coordinates of vertex and intercepts
kotegsom [21]
Te x intercepts are where the graph crosses the x axis or wher y=0
the y intercept is where the graph crosses the y axis or where x=0

to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a

so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8

vertex is (-2,-8)

intercepts
x intercept is where y=0

0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)

yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)


vertex at (-2,-8)
xints at x=\frac{-6+ \sqrt{15} }{3} and \frac{-6- \sqrt{15} }{3} or at the points ( \frac{-6+ \sqrt{15} }{3} , 0) and (\frac{-6- \sqrt{15} }{3},0)
yint at y=7 or at (7,0)
8 0
2 years ago
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