geno3141

A = (-2, -7)         B = (6, -5)         C = (5, -2)

Use the distance formula to find the three lengths AB, BC, and AC.

If all three are equal, it's equilateral; if two are equal, it's isoscles; if all are different, it's scalene.

Also, see if the three lengths fit the Pythagorean Theorem; if so, it's a right triangle.

I tried to answer it (and explain why my first answer was wrong) at the other time you asked.

Yep, the answer is 12.3°.

I forgot to check my answer. With cosine, you get two possible answers, the answer that the calculator gives you plus another answer, its supplement.

So, if you take 180° - 167.7°, you get 12.3°.

Why should you know that you need to take the supplement?

Well, if the answer is 167.7°, it is a very large (obtuse) angle, and the side opposite it must be the largest side in the triangle; it must be very large when compared to the other two sides. It isn't  -- in fact, it's the shortest side, so angle A must be the smallest angle. Then, you need to subract your answer from 180°.

OK now?

This looks as if you are using the Law of Cosines:

(3.3^2) = (5.1^2) + (8.1^2) - 2(5.1)(8.1)cos(A)

I would first calculate the numbers:

10.89  =  26.01 + 65.61 - 82.62cos(A)

10,89  =  91.62 - 82.62cos(A)

Subtract 91.62 from both sides (do NOT combine it with the -82.62!)

-80.73  =  82.62cos(A)

Divide both sides by 82.62:

-0.977124 = cos(A)

To get the size of the angle, find invCos(-0.977124), which is 167.7°

If you have any questions about any of the steps, please ask.

 5(y -1)2 - 20(x - 1)2 =64.

5(y - 1)² - 20(x - 1)²  =  64

If you place this into standard graphing form:  (y - 1)²/(64/5) - (x - 1)²/(64/20)  =  1

The distance from the center in the y-direction is √(64/5) = 8/√5.

The distance from the center in the x-direction is √(64/20) = 8√20.

The slope will be:  ±[8/√5] / [8/√20] = ±√20/√5 = ±√4 = ±2

I skipped a lot of explanation; if you want more explanation, please ask.

3x + 3 ≥ 2x + 6

x + 3 ≥ 6

x ≥ 3     --->  [3,∞)

10x + 3 > 5(2x + 1) - x + 7

10x + 3 > 10x + 5 - x + 7

10x + 3 > 9x + 12

x > 9     --->   (9,∞)

3.7 x 2 =  7.4

(3.7 x 10^4) x 2  =  (3.7 x 2) x 10^4  = 7.4 x 10^4

You can find the answer:

1) by graphing

2) by completing the square

3) by using the formula:  -b/(2a) to get the x-coordinate:

    For this problem, a = 3 and b = -12   --->   -b/(2a)  =  -(-12)/(2·3)  =  12/6  =  2

    Now, replace 2 for x in the original function, to find the y-coordinate of the vertex.

    Then you will have your vertex.

You can use the calculator at this site to figure this out.

For any problem divided by n, there cannot be more than n - 1 digits in the repeating block; thus, the answer to this problem cannot be more than 6.

6.77499EE9  = 6.77499 x 10^9

Move the decimal point 9 spaces to the right, adding zeros if necessary:

                   = 6 774 990 000