There are many reasons one may want to simplify, rearranging to find specific values - or maybe just making it simpler
Well, let's do some examples:
y(x(3+2)) +2 = -2y +2 <span>< I just made this one up, it looks really complicated right now, none the less it can be simplified easily
</span>y(3x+2x) + 2 = - 2y +2
3xy + 2xy + 2 = -2y +2
5xy + 2 = -2y +2 <-- the +2's dissapear because they cancel out
5xy = -2y
<span>And there we have it, that long expression has been simplified to something really simple.
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Another example:
3(4(x+3(2 +z)) - 5)= 3y <span><- you can start where ever, I like starting in the middle
</span>3 * (4 * (x + 3*(2 + z)) - 5 ) = 3y <span><- here it is spaced out, we get a much better view
</span><span>3 * (4 * (x + 6 + 3z) - 5 ) = 3y</span>
3 * (4x + 24 + 12z - 5) = 3y <- divide both sides by 3 ..
4x + 24 + 12z - 5 = y <- much better
<span>
</span>Note: Simplify means solving to a degree, but you can't solve it because it has unknowns
Answer: y = -x/3 + 5
Step-by-step explanation:
What we know:
- Our points are (-3, 6) and (0, 5)
First, we need to find the slope. The formula for finding slope is y2 - y1/x2 - x1.
Now, we need to plug in our values.
5 - 6/0 - (-3)
Solve.
-1/3
Our slope is -1/3.
But now we need to find the y-intercept. To do this, we will use the equation y = mx + b.
You can use either coordinate pair, but I will be using (-3, 6) first.
Plug in the values.
6 = -1/3(-3) + b
Simplify.
6 = 1 + b
Subtract 1 to both sides.
6 - 1 = 1 - 1 + b
5 = b
The y-intercept is 5. Now we can put everything together!
y = -1/3x + 5
y = -x/3 + 5
For the coordinate (0, 5), you do the same thing.
5 = -1/3(0) + b
5 = 0 + b
5 = b
y = -1/3x + 5
y = -x/3 + 5
Lets say we have a quadratic equation:
3x^2 + x + 0 = 0
Now, since if we add or subtract 0 from something, the original value stays the same, which means we can write the equation as 3x^2 + x = 0 and ignore the “+0”.
In these kinds of equations, you /can/ use the quadratic formula, but theres a much quicker way. If we factor 3x^2 + x, we get x(3x + 1) = 0. Here, x has two possible values — since the result of the multiplication is 0, that means that either one expression or the other must equal 0. In essence:
If x(3x+1) = 0 then x = 0 or 3x+1 = 0
One of the solutions is that x = 0. Lets find the other.
3x+1=0
3x= -1
x = -1/3
So x1 = 0 and x2 = -1/3. So basically you solve these equations using basic factorization. :)
Answer:
Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)
Step-by-step explanation:
