Find the value of x and the measure of angleMNQ.
1 answer:
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Answer:
Part 1) Is a inconsistent system
Part 2) Is a consistent independent system
Part 3) Is a consistent dependent system
see the attached figure
Step-by-step explanation:
we know that
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it is dependent
If a system not have solution, it is said to be inconsistent
Part 1) we have
This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept
so
The lines don't intersect
The system has no solution
therefore
Is a inconsistent system
Part 2) we have
we know that
If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution
In this problem, the lines have different slopes (m=3 and m=2)
so
The lines intersect at one point
The system has one solution
therefore
Is a consistent independent system
Part 3) we have
----> equation A
----> equation B
Multiply equation A by -2 both sides
----> equation C
Compare equation B and equation C
Are identical lines
so
The system has infinity solutions
therefore
Is a consistent dependent system
Given the two options above, in order to come up with the best plan we have to calculate the future value of money in each plan.
compound interest is given by:
Option 1
p=$500
r=2%=0.02
t=1 year
Option 2
p=$500
r=2/12=1/6
n=1*12=12
hence:
=$509.09
Comparing the two plans above, option 1 is the best.
b] Option 1 is the best because she will secure $510 as compared to option 2 which has interest rate that reduces her amount by $1 after one year due to annual charges. The total amount of money she will have at the end of the plan is $510.
compound interest is given by:
Option 1
p=$500
r=2%=0.02
t=1 year
Option 2
p=$500
r=2/12=1/6
n=1*12=12
hence:
=$509.09
Comparing the two plans above, option 1 is the best.
b] Option 1 is the best because she will secure $510 as compared to option 2 which has interest rate that reduces her amount by $1 after one year due to annual charges. The total amount of money she will have at the end of the plan is $510.