Answer:
y=ln(x/(1-x))
Step-by-step explanation:
y=e^x/(1+e^x)
Cross multiply
y(1+e^x)=e^x
Distribute
y+ye^x=e^x
Put anything with x on with side and everything without x on opposing side:
y=e^x-ye^x
Factor right hand side
y=(1-y)e^x
Divide both sides by (1-y)
y/(1-y)=e^x
Use natural log.
ln(y/(1-y))=x
The inverse is
y=ln(x/(1-x))
Putting in h(1) would get you 1, putting in h(4) would get you 5.
Answer:
6 dimes, 26 nickels
Step-by-step explanation:
The number of nickels is N, and the number of dimes is D.
N + D = 32
5N + 10D = 190
--
N + 2D = 38
D = 6
N = 26
Answer:
40.5
Step-by-step explanation:
This answer makes sense because we know that 50% of 90 is 45.
Since 45% of 90 is 40.5, we can self-check our answer.
Hope I helped!
~PumpkinSpice1♥
Answer:
-4 ± 2√6
Step-by-step explanation:
Rewritten in standard quadratic form, x^2+8x-2=18 becomes x^2 + 8x - 20 = 0.
Here the quadratic coefficients are a = 1, b = 8 and c = -20 and so the discriminant is b^2 - 4ac, or 8^2 - 4(1)(-20), or 96.
Because the discriminant is positive, we know that this quadratic has two different real roots. These roots are:
-b ± √(b² - 4ac)
x = -------------------------
2a
which in this case comes out to:
-8 ± √96 -8 ± 4√6
x = ------------------ = ------------------- = -4 ± 2√6
2 2
