Standard form: ax^2 + bx + c = y
Steps to simplify:
2x^2 - 1 = 3x + 4
~Subtract (3x + 4) to both sides
2x^2 - 1 - 3x + 4 = 3x + 4 - 3x + 4
~Simplify
2x^2 - 3x - 5 = 0
(a = 2, b = -3, c = -5)
Now that we know what these values are, we can use the quadratic formula to solve.
Answer: x = 5/2 or x = -1
Best of Luck!
1) given function
y = - 2 ^ ( -x + 2) + 1
2) domain: domain is the set of the x-values for which the function is defined.
The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.
3) x-intercept => y = 0
=> y = - 2 ^ ( -x + 2) + 1 = 0 => 2^ ( -x + 2) = 1
=> - x + 2 = 0 => x = 2
The x-intercept is x = 0
4) y-intercept => x = 0
=> y = - 2 ^ ( -x + 2) + 1= - 2 ^ ( 0 + 2) 1 = - (2)^(2) + 1 =- 4 + 1 = - 3
=> The y-intercept is - 3
5) limit when x -> negative infinite
Lim f(x) when x -> ∞ = - ∞
6) limit when x -> infinite
Lim f(x) when x - > infinite = 1
=> asymptote = y = 1
7) range is the set of values of the fucntion: y
Given that the function is strictly decreasing from -∞ to ∞, the range is from - ∞ to less than 1
Range (-∞,1)
The answer you are looking for would be 3 dollars
First, we need to find out how many houses that Hannah received money from. We can do this by dividing the total amount of money she received by the amount she received per house.
780 / 5 = 156
Hannah received money from 156 houses.
To find the amount of houses she did NOT collect money from, we just need to subtract the amount of houses that she DID receive money from away from the total amount of houses in her neighborhood.
278 - 156 = 122
Hannah did not collect money from 122 houses.
Hope this helped! =)
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