Answer:
The number of solutions to the given set of equations is 0.
Step-by-step explanation:
Number of solutions of a system of equations:
System of equations: ax = b
If a = 0 and b = 0, infinite solutions.
If a = 0 and b != 0, zero solutions.
If a != 0 and b != 0, one solution.
We are given the following system of equations:
y = 7x + 12
y = 7x + 2
So
7x + 12 = 7x + 2
7x - 7x = 2 - 12
0x = -10
a = 0, b != 0, so zero solutions.
The number of solutions to the given set of equations is 0.
Answer:
here i finished!
hope it helps yw!
Step-by-step explanation:
The doubling period of a bacterial population is 15 minutes.
At time t = 90 minutes, the bacterial population was 50000.
Round your answers to at least 1 decimal place.
:
We can use the formula:
A = Ao*2^(t/d); where:
A = amt after t time
Ao = initial amt (t=0)
t = time period in question
d = doubling time of substance
In our problem
d = 15 min
t = 90 min
A = 50000
What was the initial population at time t = 0
Ao * 2^(90/15) = 50000
Ao * 2^6 = 50000
We know 2^6 = 64
64(Ao) = 50000
Ao = 50000/64
Ao = 781.25 is the initial population
:
Find the size of the bacterial population after 4 hours
Change 4 hr to 240 min
A = 781.25 * 2^(240/15
A = 781.25 * 2^16
A= 781.25 * 65536
A = 51,199,218.75 after 4 hrs
The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.
Answer:
<em>M(13)=14.3 gram</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.
The equation of the model is:
Operating:
After t=13 minutes the remaining mass is:
Calculating:
M(13)=14.3 gram
12.60 / 7 = $ 1.80 per bottle
10.98 / 6 = $ 1.83 per bottle
18.10 / 10 = $ 1.81 per bottle
16.38 / 9 = $ 1.82 per bottle
best buy (cheapest) is : $ 12.60 for 7 bottles <==
