(3 1/2+8 2/3)-3 5/6
= 1.898717
(10 1/4 - 5 5/8)-1 3/8
= -5.221721
(2 2/3+ 4 5/6)+3 3/8
= 9.795734
Answer:
Which activities in the classroom do you enjoy the most? ...
Given a chance, what is one change that you would like to see? ...
Do you have supportive classmates? ...
What motivates you to learn more? ...
Do you think that the school provides you with adequate sports facilities?
How much time do you spend on homework every night?
Which classroom activities do you learn from the most?
What are three things that can improve the class most?
Answer:
Math has the particularity that it is a logical construction.
This means that we can start with an expression X (where X is an equation, not a variable)
Now we can apply a lot of "math" to this equation in such a way that we can rewrite it, but the actual "meaning" of the equation will not change.
An example of this is factoring.
For example, we can write a quadratic equation as:
a*x^2 + b*x + c.
And we also can write this as:
n*(x - k)*(x - j)
where k and j are the solutions of the equation:
a*x^2 + b*x + c = 0.
What is the advantage of writing the equation in each form?
Well, both expressions actually represent the same thing, but the explicit information in each expression is different, so depending on what we want to do, we will choose one option or the other.
And we have lot's of different ways to express something, where we can find some ones really complex and useful, like the series of Taylor, where we can write a function as a summation of infinite terms.
Start by writing the system down, I will use 
to represent 
Substitute the fact that 
into the first equation to get,
Simplify into a quadratic form (
),
Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,
which then must factor into
And the solutions will be 
.
Clearly for small coefficients like ours 
, this is very easy to figure out. To get 5 and 6 we simply say that 
.
This fits the definition as 
and 
.
So as mentioned, solutions will equal to but these are just x-values in the solution pairs of a form 
.
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are 
and 
.
Hope this helps :)
