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We  have

y = Acos (Bx  + C)  

A = the  amplitude =  2

Since  this is  reflected over  the x axis, we  have    A  = -2

B =   2pi  /  period  =   2pi  / 4  =   pi/2

To  find C  ....the point (.5, -2)  is on the  graph   ....so.....

-2  = -2cos (pi * .5  / 2   +  C)            divide through  by  -2

1 =  cos ( pi *.5 / 2  +  C)

1 =  cos ( pi/4 + C)

arccos(1)  = pi/4  + C

0  =  pi/4 + C

C  = - pi/4

The  function is

f(x) = -2cos ( pi * x / 2  - pi/4  )

Here's a graph :  https://www.desmos.com/calculator/eqbmyly3sk

Triangle  with  a height of 3  and a base of 7  = (1/2) 3* 7  =   21/2  = 10.5 cm^2

Square with a side of 7  = 7^2   = 49 cm^2

Area =   49  + 10.5  =     59.5 cm^2

By  the Exterior Angle Theorem

6x - 1   +  5x + 14   = 123         simplify

11x + 13  = 123

11x  =  123  -13

11x  = 110

x  = 110   /  11     =   10

H = 6 (10)  - 1   =  59°

3^(2c + 1) =  28*3^c  -  9       we can write

3^(2c+ 1)  =  (27 + 1) * 3^c  - 3^2

3^(2c + 1) =  27*3^c + 3^c - 3^2

3^(2c + 1) + 3^2  = 3^3 * 3^c + 3^c

3^(2c + 1) + 3^2  = 3^(c + 3)  + 3^c

Note  that  when c   = 2....then

3^(5) + 3^2  = 3^5  + 3^2

So....c =   2

f(x)  =  3  - 2*51^x

Range  =   (-inf, 3)

We  have    9  time periods of 20 seconds  in  3 minutes

So

275,562  =    A (3)^9      where A  is the  beginning  number

275,562  / 3^9  =  A   =   14

f '  ( x)   = ax^2  + bx

f ' (1)  = 6

a(1)^2  + b(1)  = 6

a  +  b   = 6   ⇒    b  =   6   - a       (1)

f " (x)  =  2ax  + b

f " (1)   =18

2a(1) + b  =18

2a  + b  = 18            (2)

Sub (1)  into  (2)  for  b

2a  + 6 - a   =  18

a  + 6  =  18

a  =  12

b  = 6 - 12   =   - 6

So

f'x)  =  12x^2  -  6x

f(x)  =  4x^3 - 3x^2  +  C

So

2

∫    4x^3  -  3x^2  +  C    dx  =  36

1

                            2

[  x^4 -  x^3  + Cx ]   =  36

                             1

[2^4  - 2^3  + 2C ]  -  [ 1^4 - 1^3  + C  ]   =  36

[ 16  - 8  + 2C ]  -  [ C]  =  36

8  + C  =  36

C  =  28

So

f(x)  =   4x^3  - 3x^2  + 28

I mean I do not know what the question is asking but I know the answer is x = 8/3

what??? lmao im lost

Oops! I made a mistake here; 

The correct answer is:

BD  = 24 * 2/3 = 16

BC = (16) / 1/3 = 48

DC = sqrt(48² - 16²) = 16√8

5 angle regular pentagon     ( n-2)(180) = sum of interior angles

                                                 3 * 180 = 540      so each of the five angles =   540 / 5 = 108 degrees = a

a + b are supplementary ( they add to 180)          108 + b  = 180           you can finish....right ?  

EIGHT interior angles of a 8 sided polygon shoud sum to   ( 8 -2 )(180) = 1080

    n  in the diagram = 1080 - the sum of the other given angles =.......

(a)   connect  AB

minor arc BA = 2*angle  ACB  = 2 * 37 =  74°

Since   TA  is   a tangent, then  angle  TAB  =  1/2  minor arc BA  = (1/2) (74)  = 37

So, in triangle  ABT,  angle  ABT   =  180  -  42  -  37   =   101°

(b)  Since  CA  is  a transversal  cutting parallel lines....then angles  ACB  and CAD are  equal

And  minor  arcs  BA   and  CD   are   equal  since  they are subtended by equal angles....and their  measures = 2 * 37 =  74°

And  by  the  intersecting chord theorem  angle  AEB  =(1/2) (minor arc BA  + minor arc CD) = (1/2) (74 + 74) = 74°  

(c) angle EAD  = angle  CAD  = 37°

Between 1 month and two months the charge increases 30 dollars

     so they charge 30 dollars per month      at one month the charge   is 80 dollars....30 of this is monthly charge, so 50 dollars is one-time charge

4 months should be    4 m * $ 30 /m   +  $ 50 = $170.

DC =(24 * 2/3) / 1/3 = 48

The sum of internal angles in the heptagon is 900º

x = 900 - (124+129+132+123+131+125)

x = 136º

Interior angles of an  n -polygon    sum   to ( n-2)(180)     for 7 angles    5(180 ) = 900 degrees  

     so each of the seven interior angles  = 900 / 7 = 128.57 degrees

angle n in the diagram is supplementary to this interior angle and equals  180 - 128.57 =  51.43  degrees

Look  at the second equation

y  = x  -1

y + 1  =   x                sub this into  the first equation for  x

y = 3 ( y + 1)  + 3

y = 3y + 3 + 3

y  = 3y  + 6

y  -3y  =  6

-2y   =  6

y =   6 / -2     =   -3

And   x  =  y + 1    =   -3  + 1   =  -2

(x , y)  = (-2, - 3)

idk what happened to my answer, but I meant $3\leq x \leq 7$

anyway, for the second part of the problem, the angle opposite of x will be acute only if $3^2+5^2>x^2\rightarrow\sqrt{34}>x$. For integer values, that means that it must be smaller or equal to 5.

So that means that if x is 3, 4, or 5, it will make the angle opposite of x be acute, but that doesn't mean that the triangle itself is acute. If x = 4, then it will for a 3-4-5 triangle, which is right. That means that only 3 and 5 works, so the answer is $\boxed{2}$

By the way, if you want to manually check if a triangle is obtuse or not, and you're given sides x, y, and z, then all of these these inequalities must hold true:

$x^2+y^2>z^2\\ y^2+z^2>x^2\\ x^2+z^2>y^2$

w = 12 / tan(42º) ≈ 13.3

x = 12 / tan(27º) - w ≈ 10.2

You  have  the right idea, WDB22

y changes  by  12  when  x  changes  by 4

The slope is   12  / 4    =  3

Since (3,5)  is  on the graph

y = 3 (x - 3)  +  5

y = 3x - 9 + 5

y = 3x  - 4

When x   =  0

y  = 3(0)   -4

y = 0  -  4

y  = -4

Not  as  hard  as it seems , WDB22

Look  at   the  function 

y  =  (-1/3)x   +   2

In  the form  y  = mx +  b

b  in this instance = 2   =  the y intercept

Note  that  graphs A, C  and D     have a y intercept of 2

m is  the slope  = -1/3

A negative slope  means  that the  graph "falls" as  it  goes  from left to right

Note  that only  graph D  falls from left to  right  and also has a y intercept of 2

Then....that must be the correct one....

Maybe you overthought it a bit, but I think it is just this: 

1 + y x^-1   dy/dx

   =   -1 y x^-2

    = - y/x²                                          ??

If x adds 4 when y adds 12, then if x adds 1, y adds 12/4 = 3. 

Therefore, from -1 to 0, x adds 1, and y adds 3, so the answer is -7+3 = -4