The trial and error method is used to find an initial factor:
If we let f(x) = x³ - x² - 24x - 36 and all we have to do is sub' in values of x until
f(x) = 0, we can use this to find an initial factor by the factor theorem:
f(1) = (1)³ - (1)² - 24(1) - 36 = -60
f(2) = (2)³ - (2)² - 24(2) - 36 = -80
f(5) = (5)³ - (5)² - 24(5) - 36 = -56
*** f(6) = (6)³ - (6)² - 24(6) - 36 = 0 ***
f(6) = 0 so (x - 6) is a factor of f(x).
This means that: f(x) = x³ - x² - 24x - 36 = (x - 6)(ax² + bx + c).
To find a,b and c, use long division (or inspection) to divide x³ - x² - 24x - 36 by x - 6.
The other 2 factors of f(x) can then be found by factorizing the
ax² + bx + c quadratic the way you would with any other quadratic (i.e. by quadratic formula, CTS or inspection).
for these you need to rearrange the equations and do substitutions.
#3 = if x+y=5 then you know x = 5-y
now substitute that equation for x in the 2nd one so x + 2y = 8 becomes
5-y + 2y = 8 2y - y becomes 1y which becomes y then subtract 5 from each side to get y =3
now replace y with 3 in the first equation x = 5-3 so x = 2
so (2,3) is the answer
same type of work for #4
2x-y=6 ,S0 y = 2X+6
so now you have 4x+2(2x+6)=-4
that becomes 4x +4x+12 = -4
8x+8 = 1, x =1
y = 2(1)-6 = -4
so answer is (1,-4)
Answer:
Explanation:
The <em>end behavior</em> of a <em>rational function</em> is the limit of the function as x approaches negative infinity and infinity.
Note that the the values of even functions are the same for ± x. That implies that their limits for ± ∞ are equal.
The limits of the quadratic function of general form 
as x approaches negative infinity or infinity, when 
is positive, are infinity.
That is because as the absolute value of x gets bigger y becomes bigger too.
In mathematical symbols, that is:
Hence, the graphs of any quadratic function with positive coefficient of the quadratic term will have the same end behavior as the graph of y = 3x².
Two examples are:
Answer:
The first event is represented by a dot. From the dot, branches are drawn to represent all possible outcomes of the event. The probability of each outcome is written on its branch.
Step-by-step explanation:
Answer:
3 : 1
Step-by-step explanation:
We have to compare the value of two sides.
Ratio of sides = 12 : 4 = 
= 3 : 1
