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
Answer:
Choice A is correct; Kindly rate
Step-by-step explanation:
A function is said to be increasing over a given interval if the value of the function is increasing over the said interval. From the graph, the function is increasing over the interval since with every change in the x-value, the y-value is increasing
Answer:
4 seconds
Step-by-step explanation:
When the ball is on the ground h = 0, hence
- 16t² + 64t = 0 ( solve for t )
factor out - 16t
- 16t(t - 4) = 0
equate each factor to zero and solve for t
- 16t = 0 ⇒ t = 0
t - 4 = 0 ⇒ t = 4
the 0 solution is the height of the ball before being hit and
the time the ball takes to hit the ground is 4 seconds
Answer:
V= area of cross-section x length
V = 0.5x(8x9) x 11
V = 396cm^3
Hope this helps!
