Answer:
<A = 27 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
Tan A = opp side / adj side
Tan A = 2/4
Tan A = 1/2
Taking the inverse tan of each side
tan^-1 ( tan A) = tan ^-1 (1/2)
A =26.56505118
Rounding to the nearest degree
A = 27
The general way to work this out is to solve the general expression for
the remaining quantity versus half-life, using logarithms. But that's not
necessary with these numbers.
Look at the numbers:
-- 3 mg is 1/4 of 12 mg.
-- 1/4 is the product of (1/2) x (1/2).
-- So the 3 mg is what's left of 12 mg after 2 half-lives.
The 26 minutes must be two half-lives.
-- The half-life of that substance is 26/2 = <em>13 minutes</em>.
Go Maggie !
Let

denote the number of minutes spent brushing his teeth, and let

be the mean and

the standard deviation for this distribution.

The z-score corresponding to this probability is approximately

, which means

Next, (note the sign change)

The corresponding z-score is approximately

, so you have

Solving the two equations for

and

, you'll find that the mean is approximately

and the standard deviation is approximately

.
Answer:
, 
Step-by-step explanation:
One is asked to find the root of the following equation:

Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:

Change the given equation using inverse operations,


The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:

Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,


Simplify,



Rewrite,

, 
x = 8
Solution:
Side-splitter theorem:
<em>If a line is parallel to one side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally.</em>

Do cross multiplication, we get
⇒ 4 × 42 = 21x
Divide by 21 on both sides, we get
⇒ 4 × 2 = x
⇒ 8 = x
Switch the sides.
⇒ x = 8
The value of x is 8.