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
What I always do to solve this, is find a common factor for each number first.
Usually 4 or 5 works best. I'll use 4.
4 goes into 80 20 times, which means that 4 = 5% of 80.
If 4 = 5%, and 48 = 12 x 4, then 48 must equal 60% of 80.
(Another way to solve this problem is: simplify 48 / 80. This simplifies to 3/5.
3/5 = 60%)!
Answer:
By using the energy conservation law, the input energy must be equivalent to the output energy. If you measured output energy is lower than your input energy, you have lost that difference of energy either in mechanical inefficiency (friction, heat, etc.) or an energy sink.
Thus, the energy not output by the machine is lost in the process within the machine.
Cheers.
No it is not because its more then ten numbers away from the solution of the five tickets
