Answer:
2.25
Step-by-step explanation:
The solution depends on the value of
. To make things simple, assume
. The homogeneous part of the equation is
and has characteristic equation
which admits the characteristic solution
.
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
. Then
So you have
This means
and so the general solution would be
The first 3 are examples of the difference of 2 squares so you use the identity
a^2 - b^2 = (a + b)(a - b)
x^2 - 49 = 0
so (x + 7)(x - 7) = 0
so either x + 7 = 0 or x - 7 = 0
giving x = -7 and 7.
Number 7 reduces to 3x^2 =12, x^2 = 4 so x = +/- 2
Number 8 take out GCf (d) to give
d(d - 2) = 0 so d = 0 , 2
9 and 10 are more difficult to factor
you use the 'ac' method Google it to get more details
2x^2 - 5x + 2
multiply first coefficient by the constant at the end
that is 2 * 2 = 4
Now we want 2 numbers which when multiplied give + 4 and when added give - 5:- -1 and -4 seem promising so we write the equation as:-
2x^2 - 4x - x + 2 = 0
now factor by grouping
2x(x - 2) - 1(x - 2) = 0
(x - 2) is common so
(2x - 1)(x - 2) = 0
and 2x - 1 = 0 or x - 2 = 0 and now you can find x.
The last example is solved in the same way.
Answer:
y = 6
Step-by-step explanation:
line of an equation: y = mx +c
where c is y-intercept, m is gradient and y and x are the y and x coordinates.
For finding the line of an equation we first find a gradient
gradient = (y2 -y1) / (x2 - x1)
so; (6-6) / (7-(-5)) = 0/12 = 0
next using any pair of coordinates we will find the c (y-intercept)
6= 0 (-5) + c
c = 6
so the equation will be
y = mx + c
(add the values you just found)
y = (0)x + 6 (since anything multiplied by 0 is 0 so we can write its like;)
y = 6
The economic term used to describe a period of sustained increase in the prices of goods and services is called inflation. Inflation is characterised mainly by a general increase in the prices of goods and services and a reduction in the currency's purchasing power. Hope this helps. Let me know if you need additional help!
