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
Answer:
3x + 4.5x + 1 = 28
3.6 seconds
Step-by-step explanation:
Initial distance apart = 1 foot
Student A:
Walk rate = 3 ft per second
Student B:
1.5*3 = 4.5 ft per second
How long it will take to be a total of 28 feets apart
Distance = speed * time
Let time = x in seconds
Student A distance = 3x
Stident B distance = 4.5x
Initial distance = 1 foot
3x + 4.5x + 1 = 28
7.5x = 28 - 1
7.5x = 27
x = 27/ 7.5
x = 3.6 seconds
You have to consider the “ends” of the x-axis, the far right (for infinitely large values of x) and left (for infinitely small values of x) of the graph.
From the diagram above you can see that:
- When
then 
(notice that as the values of x get smaller and smaller, the graph gets closer and closer to the line y=1); - When
then 
(notice that as the values of x get larger and larger, the graph gets closer and closer to the line y=1).
Answer: correct choice is D.
Step-by-step explanation:
The expressions are not properly written
Given
RS = 4x – 9
ST = 19
RT = 8x – 14
Based on the given parameters, the addition postulate below is true
RS+ST = RT
Substitute
4x-9+19 = 8x-14
collect like terms
4x-8x = -14-19+9
-4x = -33+9
-4x = -24
x = -24/-4
x = 6
Get RS:
RS = 4x-9
RS = 4(6)- 9
RS = 24-9
RS = 15
Get RT:
RT = 8x - 14
RT = 8(6)-14
RT = 48-14
RT = 34
