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We need to solve this

f(g(x))  =  g (f (x))

2(3x + c) + 7    = 3(2x + 7)  + c          simplify

6x + 2c + 7  =  6x + 21  + c      subtract  6x  from both sides

2c + 7  =  21 + c         subtract c , 7  from both sides

c  =  14

-548

720 - 548  =   172°

-532

720 -548  =  188°

-188

360 -188  = 172°

8     =    8°

532

532 - 360  = 172°

We  have  a 30-60-90  right triangle

Side  opposite 60° angle =  15

Side opposite of 30°  angle =  15/√3

Side opposite the 90° angle  = 2 times the side opposite the 30° angle = 2*15 / √3  =  30 / √3 = the hypotenuse

Set up variables

Length = 6x

Width = 3x

Height = 6x - 3

Commence calculations

For surface areas:

L * W surfaces = \(36x^2\)

L * H surfaces = \(72x^2-36x\)

W * H surfaces = \(36x^2-18x\)

Set up equation

\(144x^2-54x = 100\)

\(144x^2-54x - 100 = 0\) divide by 2

\(72x^2-27x-50=0\)

72x^2-27x-50=0 = {x=(25/24), x=-((2/3))}

So \(x=25/24\)

now solve for height

Well it is a 30-60-90 triangle.

Tell me what you are confused on

Good work to both of you!!!

This is what the cutting is? Im just gonna solve it like that...

Now we turn the cube on its cut face (i suck at drawing so its hard to comprehend). Imagine that the cut face (triangle) is on the table.

Commence calculations

Sorry this may be EXTREMELY difficult to comprehend because I suck at drawing lol

Hypotenuse = \(\sqrt{2}\)

Long Leg = \(\frac{\sqrt{6}}{3}\)

By pythageoran theorem:

Answer = \(\sqrt{(\sqrt{2})^2-(\frac{\sqrt{6}}{3})^2}\)

We get a radical of

\(\boxed{\frac{2\sqrt{3}}{3}}\)

Thanx, MathGuru !              ......gotta go shovel snow...wooohooo!

transcription ?       I am not sure I remember......

FAT in ingredients    = fat in final solution

x = 6% amount

   then   60 - x   = 3% amount

6% (x)   +  3% (60-x)   = 4% ( 60)

.06 x       + .03 (60-x)   = .04 (60)        solve for 'x' the amount of 6%    then  3% amount =   60-x

Assume this is

tan (-2pi/3)

_________ -  sec (-pi)         ???   .....if  so, we have ....

sin (7pi/4)

-2pi/3  =  -120° = (360 - 120)°  = 240° = 60° in Q3  =  tan (60)  = √3

7pi/4 * 180/pi  =  7 *(180/4)  =  7 * 45  =  315° =  45° in Q4

So    sin (-45°) = -√2/2

sec (-pi)  =  sec (pi)  = -1

So we have

  √3

_____ -  (-1)  =

  √2/2

2√3

___  +  1   =

 √2

2√3 * √2

_______  +  1     =

 √2 * √2

2√6

___  +    1   =

  2

√6  +  1

In triangle \(ABC\), \(AP = BQ = \frac{PQ}{2}\) and \(CR/RA = 3/2 \). Find the ratio of the area of triangle \(BQC\)  to the area of triangle \(CRQ\).

Since AP = BQ = PQ/2. We can conclude that QB is 1/4 of AB.

Let the area of ABC = x

So BQC = \(\frac{x}{4}\)

Area of triangle CAQ = \(x-\frac{x}{4}=\frac{3x}{4}\)

Since CR/RA = 3/2, that means that CRQ = \(\frac{3x}{4}*\frac{3}{5}=\frac{9x}{20}\)

SO

Area of BQC is \(\frac{x}{4}\)

Area of CRQ is \(\frac{9x}{20}\)

Can you find the ratio now? (Hint: It's simple algebra!)

I THINK you mean    -7 , - sqrt 23       this is in Quadrant III      sin and cos will be negative

    the point describes a right triangle with the x-axis

       hypotenuse (using Pythag Theor)

             =        hyp^2 =  (-7)^2  + (-sqrt 23)^2

                       hyp = sqrt 72

cos = adj / hyp     =  - 7 / sqrt(72)        and simplify......

Answered here :

https://web2.0calc.com/questions/right-efg-has-its-right-angle-at-f-eg-10-and-fg-4#r1

−11π12

2pi - 11pi/12  = 

[24pi]/12 - [11pi]/12  =

13pi/12  *  180/pi  =

(13) (180/12)  =

13 * 15 =

195°  =   15°  in the 3rd quadrant

−23π6

4pi - 23pi/6 =

(24pi)/ 6 - (23pi)/6 =

pi/6  =  30°   in the first quadrant 

7π6

7pi/6  * 180 /pi  =   

7 (180/6) =

7* 30 =

210°

And  210  - 180  = 30°  in the 3rd quadrant 

OK

2sqrt (15)  = sqrt (60)

2sqrt (6)  = sqrt (24)

The  other leg  =    sqrt  [ (sqrt (60))^2  - (sqrt (24))^2 ]  = sqrt  [ 60 - 24 ]  = sqrt (36)  = 6= the longer leg

The larger angle [call it A ] is opposite the longer leg....so we can use the tangent to find this angle

tan A =  6 / sqrt (24)      and using the tangent inverse to find  A

arctan (6/ sqrt (24)) = A   ≈  50.8°

Call the number of  bike rentals  = x

And the number of skate rentals =  20 - x

So

25x   + 20 ( 20 - x)   = 455     simplify

25x + 400 - 20x  = 455

5x + 400 = 455     subtract 400 from both sides

5x  = 55     divide both sides by 5

x  =11   = number of  bike rentals

Sorry! I fixed it

No  number of centimeters  displays  (for me, anyway  )

Good work, EP    !!!!

Perimeter  =  2 (W + L)

So

312  = 2 (63 + L)     diviede both sides  by 2

156  = 63 + L      subtract 63 from both sides

93  = L

The cotangent function is defined as the length of the side adjacent over the length of the side opposite.

9 / [ sqrt (3) / 2 ]  =

(9/1) * (2 /sqrt 3 )  =

18 / sqrt 3  =

18 sqrt (3 ) / 3  =

6sqrt (3)