NinjaDevo

This equation is quite similar to this one: 

Check:

6(-4/3)²+5(-4/3)-4=0

6(16/9)+(-20/3)-4 = 0

(96/9)+(-60/9)-4 = 0

36/9 - 4 = 0

4-4 = 0

0=0 ✓

6(1/2)²+5(1/2)-4=0

6(1/4)+5/2-4 = 0

1.5 + 2.5-4 = 0

4-4=0

0=0   ✓

Find all solutions for x: 6x²+5x-4=0

We can start by factoring this polynomial.

 6x²+5x-4=0

(3x + 4)(2x - 1) = 0

This means that (3x + 4) = 0 and (2x - 1) = 0

Let's start with the first solution for x:

(3x + 4) = 0

-4             -4             ---Subtract 4 from both sides

3x = -4

÷3      ÷3           ---Divide 3 by both sides

x = -4/3

And now our second solution:

(2x - 1) = 0

       +1    +1        ---Add 1 to both sides

2x = 1

÷2      ÷2              ---Divide both sides by 2

x = 1/2

There we go! Our two solutions for x are: x = 1/2 and x = -4/3.

20,938,479,392*120,932,843,890 = 2,532,149,859,606,718,114,880

-9/0

-9/1 ÷ 0/0

-9/1 * 0/0

-0/0

= 0

I'm not entirely sure if this is correct because I tried it on two different calculators. One said ERROR and the other one said -Infinity.

...?

Good one CPhill,

I'll have to remember that for the next time I write a long explanation. :)

Sorry for the long explanation, I kind-of wrote you a book here. :)

We have 6.9*x-6=9, and we need to solve for x.

6.9*x-6=9

        +6   +6          ---Add 6 to both sides, we can do this as long as we make sure to do it to both sides.

6.9*x = 15            

÷6.9      ÷6.9          ---Divide both sides by 6.9. Again, this works aslong as it is done to both sides of the equation.

Now we are left with:

x = 2.173913

or we can round this up to 

x = 2.2

Let's check it. To check it, we can put in 2.173913 for x, because x = 2.173913.

6.9*(2.173913)-6=9

14.999999-6 = 9           ---14.999999 is sooo close to 15, that we can round it up to 15.

15-6=9

9=9 ✔

9 does equal 9, so our answer is right!

When we are trying to find a scale factor, we will have two objects that are basically the same, but one is bigger than the other.

(note: these squares are not to scale)

The scale factor is simply what we could multiply one of the objects by to get the other one. For example, if we had the area of the square on the right, we could multiply the scale factor to find the area of of square on the left.

Now, your asking, how do we find the scale factor?

We need to find an corrosponding legnth from our squares, and make it a ratio.

So we can look at our example here, and we can see that the first square last a legnth of 1, whereas the second square has a legnth of 5. Let's make this a ratio!

1/5

This is basically saying that the first square is 1/5 the size of the second square. And it is our scale factor.

The scale factor could also be 5/1, or just 5, and this is just saying that the second square is 5 times the size of the first square.

How we might use this scale factor is to find the height of the second square in the example picture. The height is unknown (x), but we can figure this out.

We know that the first square is 1/5 the size of the second square, or in other words, the second square is 5 times bigger than the first square. Knowing this we could multiply the hieght of the first square(4) by 5 to find the height of the second square, so the height of the second square is 20!

Also, scale factors doesn't have to just apply to squares, it can apply to triangles, circles, etc!

You know it's a good day on the forum when people are fighting over each other to answer questions though, right?