Find the two angles that satisfy the equation.

3a. sin(3x + 2)° = cos(x + 44)º.

3b. sin(2x + 20)° = cos(3x + 30)".

3a. 35°, 55°     3b. 36°, 54°

Step-by-step explanation:

3a. sin(3x + 2)° = cos(x+44)°

Since sine and cosine are based upon right triangles, the two angles must add up to 90°. Thereby, 3x+2 +  x+44 = 90. Combine like terms to get:

4x + 46  =  90       subtract 46 from both sides

   -46     -46

4x          = 44        divide both sides by 4

4                4

x    =   11          plug that back into both angles

3(11) + 2 = 35°;   11 + 44 = 55°

3b. In your equation, (2x+20) + (3x+30) = 90. Combining like terms gives you:

5x + 50  =  90     subtract 50 from both sides

     - 50     -50

5x  =  40        divide both sides by 5

5         5

x   =  8      plug that back into both angles

2x+20 = 2(8) + 20 = 36°

3x+30 = 3(8) + 30  = 54°

The two angles are 36° and 54°

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .