To solve any equation, we have to get the variables and the constants (numbers) on opposite sides of the equals sign.
First, we have to combine the like terms on the left side of the equation, resulting in
7a - 9 = 30
Then, because we want the constants on the right side of the equation, we have to +9 to cancel out the -9 on the left side.
7a=39
Next, the a has a coefficient of 7, which it is multiplied by. To undo multiplication, you have to divide. Therefore, we should divide both sides by 7.
a= 5 4/7 or 5.57142857143
In improper fraction form, a = 39/7, as this fraction cannot be simplified any farther.
This can be expanded through the tangent angle addition formula:
tan(α+β)=tanα+tanβ1−tan -α + tanβ
Thus,tan(x+y)=tanx+tany1−tan x tany
Hope it helps you
Let L represent the ladder length, and x the distance the horiz. ladder reaches out from the wall. Then L = x + 3, where x is the distance of the bottom of the ladder from the wall when the top of the ladder is 9 ft. above the ground.
Consider the triangle formed by the hypotenuse (L, same as ladder length), the (vertical) side opposite the angle formed by the hypo. (with length 9 ft) and the horiz side (which we will call x). Then, according to the Pythagorean Theorem,
L^2 = x^2 + 9^2. But L = x + 3, and L^2 = x^2 + 6x + 9 = x^2 + 9^2. Solving this equation results in x=3. 6x + 9 = 9^2, or
6x + 9 = 81
6x = 72
x = 12
But L = x+3. So L=12+3, or L = 15 (feet).
The distribution lies within one of the standard of deviation of the mean so <span>68% </span>
The distribution lies within two of the standard of deviations of the mean so 95%
The distribution lies within three of the standard of deviations of the mean so 99.7%
