Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
Given:
a.) The population of Arizona is estimated to increase by 6.2% every year.
b.) The population was 4.18 million in 2016.
For us to be able to determine the population in 2022, we will be using the following formula:
Where,
P = Total population after time (t)
P₀ = Starting population = 4.18 million
r = Growth rate (in decimal form) = 6.2%/100 = 0.062
t = time (in years) = 2022 - 2016 = 6 years
e = Euler's number = 2.71828182845
We get,
Therefore, the population in 2022 will be approximately 6,063,646.
Answer:
the answer would be 81
Step-by-step explanation:
6 to the second power would be 36 then you would multiply 36x2 and it would equal 72. then you would do 2x6 which is 12. then 72+12-3= 81
-8r^5+23r^3-11r+17
Wasn’t Sure What It Was Asking So Hopefully That Works For You
Answer:
Step-by-step explanation:
Please use " ^ " to denote exponentiation: f(x) = x^2 + 4x - 21.
This function has a graph which is a parabola that opens up.
Its vertex is found by completing the square:
x² + 4x + 4 - 4 - 21, or
(x + 2)² - 25
Comparing this to the standard equation
(x - h)² + k, we see that h = -2 and k = -25.
Thus, the vertex (and the minimum of this function) is (-2, -25).
Thus, the range is [-25, ∞ ). This being a polynomial function, it has no restrictions on the domain: the domain is (-∞, ∞ )
