Answer:
and 
.
Step-by-step explanation:
So I believe the problem is this:
where we are asked to find values for 
and 
such that the equation holds for any 
in the equation's domain.
So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).
In other words this will clear the fractions.
As you can see there was some cancellation.
I'm going to plug in -7 for x because x+7 becomes 0 then.
Divide both sides by -10:
Now we have:
with
I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.
Divide both sides by 10:
So and .
The "m" in y = mx + b is the <u>slope.</u>
It is the number of units a point goes up, down, left, or right each time. Making the line linear/straight.
"rise" is the the number of units you go up(+) or down(-), "run" is the number of units you go to the right
For example, if your slope is:
You are going up 1 unit, and to the right 2 units
3 or 
You are going up 3 units, and to the right 1 unit
You are going down one unit, and to the right 2 units
-3 or 
You are going down 3 units, and to the right 1 unit
Parenthases
Equation
Multiplication
Division
Addition
Subtraction
Answer:
3x + 4 = 12 :- x = 8 / 3
Step-by-step explanation:
3x + 4 = 12
Move all terms not containing x to the right side of the equation.
Subtract 4 from both sides of the equation.
3x = 12 - 4
Subtract 4 from 12.
3x = 8
Divide each term by 3 and simplify.
Divide each term in 3x = 8 by 3.
3x / 3 = 8 / 3
Cancel the common factor of 3.
Divide x by 1.
x = 8 / 3
The result can be shown in multiple forms.
Exact Form:
x = 8 / 3
Decimal Form:
x = 2.6
Mixed Number Form:
x = 2 2/3
cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>)
So if both cot(<em>θ</em>) and cos(<em>θ</em>) are negative, that means sin(<em>θ</em>) must be positive.
Recall that
cot²(<em>θ</em>) + 1 = csc²(<em>θ</em>) = 1/sin²(<em>θ</em>)
so that
sin²(<em>θ</em>) = 1/(cot²(<em>θ</em>) + 1)
sin(<em>θ</em>) = 1 / √(cot²(<em>θ</em>) + 1)
Plug in cot(<em>θ</em>) = -2 and solve for sin(<em>θ</em>) :
sin(<em>θ</em>) = 1 / √((-2)² + 1)
sin(<em>θ</em>) = 1/√(5)
