Answer:
~1.8 mile
Step-by-step explanation:
Michael lives at the closest point to the school (the origin) on Maple Street, which can be represented by the line y = 2x – 4.
This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.
Denote equation of y2 is y = ax + b,
with a is equal to negative reciprocal of 2 => a = -1/2
y2 pass the origin (0, 0) => b = 0
=> Equation of y2:
y = (-1/2)x
To find location of Michael's house, we get y1 = y2 or:
2x - 4 = (-1/2)x
<=> 4x - 8 = -x
<=> 5x = 8
<=> x = 8/5
=> y = (-1/2)x = (-1/2)(8/5) = -4/5
=> Location of Michael' house: (x, y) = (8/5, -4/5)
Distance from Michael's house to school is:
D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) = ~1.8 (mile)
for f(x) = -2(x-4)2+2 - set equation to y = -2(x-4)2+2, solve x-4=0, x = 4
axis of symmetry is x = 4
for g(x) = 5x2-10x+7, set equation to y = 5x2-10x+7, solve the square: 5x2 becomes 5(x-1)2 solve x-1 = 0, x = 1
axis of symmetry is x=1
for H(x) what x value would be the centerline so that the graph symmetry is the same on both sides? looking at the graph the top of the arc is on -2
so axis of symmetry is x = -2
50000 + 3000 + 900 + 60 + 1
That is the expanded form
so amnt of money is x
x - 5 is Mark's remaining amnt
x - 20 is Susan's remaining amount
x - 5 = 2( x - 20) as he has twice the amnt of Susan
x - 5 = 2x - 40
40 - 5 = 2x - x
35 = x
the original amnt is $35
