First find the slope of f(x).
m=(y2-y1)/(x2-x1)
m=(1-5)/(2-0)
m=-4/2
m=-2
y=-2x+b, using (2,1) we can solve for the y-intercept, "b"
1=-2(2)+b
1=-4+b
5=b
y=-2x+5
So f(x) has a y-intercept of 5
g(x)=6m+3
So g(x) has a y-intercept of 3
h(x)=3x+4
So h(x) has a y-intercept of 4
Then g(x) has the lowest y-intercept of just 3.
Quarters = x
dimes = 196 - x
10(196 - x) + 25x = 3940
1960 - 10x +25x = 3940
1960 + 15x = 3940
15x = 1980
x = 132
169 - 132 = 64
Therefor there are 132 quarters and 64 dimes
Answer:
218
Step-by-step explanation:
Because we need f(n) to calculate f(n+1), we have to calculate our values one step at a time. Starting with f(1) = 1,
f(2) = 5(f(1)) + 3 = 5(1) + 3 = 5+3 = 8
f(3) = 5(8) + 3 = 40 + 3 = 43
f(4) = 5(43) + 3 = 215 + 3 = 218
X = short section of rope
4x = longer section of rope
x + 4x = 25
5x = 25
x = 5
…or in other words the shorter piece of rope is 5 feet long