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sin(theta + beta) = sqrt(2)/7

a₁₃₉ =  a₁  + d ( n  -1)

So we have

a₁₃₉ =  -28  - (1/3) ( n - 1)

a₁₃₉  = -28 - (1/3)(139) + 1/3   =  -28 - 139/3 + 1/3  =  -28   -  138/3  =  -28 - 46  =  - 74

x^2 + y^2   = 2x - 6y + 6       rearrange as

x^2 - 2x   +  y^2  +  6y  =   6      completete the square on  x and  y

x^2 -2x + 1   +  y^2  + 6y + 9  =  6 + 1 + 9

(x -1)^2  +  ( y + 3)^2   =  16

This is a circle  centered at   (1, -3)   with a radius  of  4

The  area  is

pi r^2  =     pi * 4^2 =    16 pi units ^2

The region is a circle with radius sqrt(12), so the area is 12*pi.

i dont know what that is so could you help me out?

2. Angle GXH = 12 degrees

3. The distance from E to line AC is 14.

These vertices form a right triangle with sides RS and RT; one will be the base, the other will be the height.

Find these two lengths and use the formula:  A  =  ½·base·height

Since you know the dimensions of the rectangular prism, find its volume:  V = l·w·h.

Then, multiply this value by its density to find the number of grams.

1. The distance from E to line AC is 18.

2. The hypotenuse is 17*sqrt(5).

3. The area of rectangle WXYZ is 112*sqrt(3).

Step 1:  Since you know the three sides of the triangle, use the Law of Cosines to find the size of angle(B).

Step 2:  Now, using angle(B), AB and BM, use the Law of Cosines to find AM.

x = y^2 -8y  + 13        a = 1    b = -8        y of vertex = -b/(2a)      then plug this value in to find 'x'

Find the 'x' value of the vertex = - b/(2a)       a = -2  b = 8

    plug this value in to find the 'y' value

First:  find the y-value when x = 2:     y  =  16(2) - 12(2)² + 2  =  -14   --->   (2, -14)

Second:  in order to find the slope of the line, find the first derivative of y:

      y'  =  16 - 2·12x     --->     y'  =  16 - 24x

At x = 2   --->   y'  =  16 - 24·2  =  -32

You know have both the point and the slope at that point; use the point-slope form:

     y - -14  =  -32(x - 2)

Draw a diagram ...

Straight acroos from Ezra to Allie's flagpole is 15 feet.

From that point on Allie's flagpole up to Allie is 35 - 27 = 8 feet.

You have now drawn a right triangle with its two sides 15 feet and 8 feet; use the Pythagorean Theorem to find the hypotenuse.

4y - 4x²  =  1   --->   y - x²  =  1/4                      (note that y must be positive)

4x - 4y²  =  1   --->   x - y²  =  1/4                      (note that x must be positive)

Setting these two equations equal to each other:

      y - x²  =  x - y²

     y² + y  =  x² + x

Completing the square:

    y² + y + 1/4  =  x² + x + 1/4

        (y + 1/2)²  =  (x + 1/2)² 

Taking the square root of both sides (ignoring negative possibilities):

        y + 1/2  =  x + 1/2

                 y  =  x

Since  4x - 4y²  =  1   --->   4x - 4x²  =  1   --->   x² - x - 1/4  =  0

                                  --->   (x - 1/2)²  =  0   --->   x  =  1/2     and     y  =  1/2

x³ + y³  =  (1/2)³ + (1/2)³  =  1/4

1 / (1/4)  =  4

1/a + 1/b = 2/17

b/ab+a/ab=2/17

a+b/ab=2/17

17(a+b)=2ab

17a+17b=2ab

2ab-17a-17b=0

Multiply the equation by two...

4ab-34a-34b=0

If 289(17^2) is added to both sides, then (2a-17)(2b-17)=289.

289=1*289 and 17*17.

2a-17=1  

2a=18   a=9              2b-17=289   2b=153             (9,153), (153,9)

2a-17=17  2a=34  a=17            2b-17=17,  2b=34, b=17            (17,17)

Thus, there should be three(3) positive ordered pairs.

The exterior angles of a triangle are in the ratio 3:4:5  What is the measure (in degrees) of the least interior angle of the triangle? 

Well, a triangle doesn't have exterior angles, but if it did they'd be vertical angles of the interior angles and therefore the same.  So let's figure the interior angles of a triangle in the ratio 3:4:5. 

3 + 4 + 5 = 12 so there are 12 parts to divvy up.  Since the interior angles of a triangle total 180^o, each part equals 180/12 which is 15. 

So             3 x 15 = 45^o 

and           4 x 15 = 60^o 

and           5 x 15 = 75^o 

And there you go, your three angles in the ratio 3:4:5 and the smallest one is 45^o  

_.

This might help! https://www.khanacademy.org/science/ap-physics-1/ap-one-dimensional-motion/average-and-instantaneous-acceleration/v/acceleration

I think you can use the acceleration formula! You can do some research because that is how we learn! (There are great lessons about it on khan academy, not an advert). :)

tan 10 = h/(x+800)    h = (x+800) tan 10

tan 24 = h/x              h = x tan 24

x tan 24 = (x+800) tan 10      solve for   x  = 524.584

tan 24 =  h/ 524.584          h = 233.56 ft

69/420 feet