What is the common difference between the terms in this arithmetic sequence?
1 answer:
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to find the point, find the location
realize that the shortest line that crosses through the origin and y=9x+8 is perpendicular to y=9x+8
perpendicular lines have slopes that multiply to get -1
y=9x+8 has a slope of 9
9*m=-1, m=-1/9
the slope of the mystery line is -1/9
since it passes through the origin, the y intercept is 0
y=(-1/9)x is the equation of the line from the point to the origin
find the intersection of this line and the original line
set them equal to each other
(-1/9)x=9x+8
multily both sides by 9
-x=81x+72
minus 81 both sides
-82x=72
divide both sides by -82
x=-36/41
find y
y=(-1/9)x
y=(-1/9)(-36/41)
y=4/41
the point is
Answer: (3) f(8) = g(8)
<u>Step-by-step explanation:</u>
Let's compare the values of f(x) and g(x) when x = 0, 2, 8, and 4
<u> f(x) </u> <u> g(x) </u> <u>Comparison</u>
f(x) = 2x - 3
f(0) = 2(0) - 3
= -3 = 1 f(0) < g(0)
f(2) = 2(2) - 3
= 1 = 4 f(2) < g(2)
f(8) = 2(8) - 3
= 13 = 13 f(8) = g(8)
f(4) = 2(4) - 3
= 5 = 7 f(4) < g(4)
The only statement provided that is true is f(8) = g(8)