Answer:
The spy must have at the start the amount of $1,024 in order to escape
Step-by-step explanation:
Let
a ------> amount of money that the spy must have at the start to escape
y ----> the remaining money
x ----> the number of guards
In this problem the remaining money is going to be reduced by half, every time the spy passes through a guard, so we can use an exponential function of the form
where
a is the initial value (amount of money at the start)
b is the base
b=(1-r)
r is the rate of decay
In this problem we have
r=50% -----> r=0.50
The value of b is
b=(1-0.50)=0.50
substitute
we know that
In order to escape after the fourth guard the amount of money remaining must be equal to $64
so
For x=4, y=$64
substitute in the equation and solve for a
therefore
The spy must have at the start the amount of $1,024 in order to escape
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
----------------------
To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
------------------------
Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).
When you convert it you'll get 240,000 cg
A = P(1 + r/n)^(nt)
<span>A = 7300(1 + 0.07/2)^(2)(3) = 7300(1.035)^6 = 7300(1.2293) = $8973.56 </span>
<span>A = 2100(1 + 0.094/4)^(4)(2) = 2100(1.0235)^8 = 2100(1.2042) = $2528.84 </span>
