ilorty

You could do that, it definately works. If following your way, we would use the difference of squares. But, that would be long and messy.

Instead, we can say that x^2=y, and swap y^2 for x^4.

We get y^2=-4.

So, y is -2i and 2i.

Now, we see that x^2 is -2i and 2i. After solving, the final answers are: x=1+i, x=-1-i, x=-1+i, x=1-i

:)

Let's create a variable for x^2. We can store that as y.

So, our new equation is y^2+y+1=0.

From here, we see that y is y=(−1−i√32)/2,(−1+i√32)/2.

Then, square root the two roots, and you will get the answer!

:)

I don't see a range for x exactally, I only see one value. But, to find that value, we will solve this equation:

3x-9=180-93 (180 degrees in a straight line)

3x=180-93+9

3x=96

x=32.

I only see 32 as an option for x. Is there something I'm missing?

Edit: Forgot to add!  Credit: gwenspooner85

:)

We can rephrase the question, and say: Out of 7 points, how many ways can we choose 3? The key word here is "choose". This tells us to use the choose formula.

What you should do is solve for 7 choose 3. 

For a number to be divisible by 5, it has to end in a 0 or 5. Also, a 4 digit number can't start with 0. 

We could do casework. Case 1, where it ends in 0, Case 2, where it ends in 5.

Case 1:

3*2*1*1

That gives us 6. Divide by 2!, and we get 3.

Case 2:

2*2*1*1

Divide by 2!, and we get 2.

2+3 is 5. Therefore, there are 5 ways to arrange the numbers.

Hint: Try using angles and line measures (and some geometric intuition) to find the ratio of ET to TC

Extra hint: (congruent triangles/similar triangles?)

Even more extra hint: Look at triangles EST and TRC

Even even more extra hint: How do we find out what shape SDRQ is?

(If you still need help, just ask me!)

:)