Ans(a):
We know that a function can't have repeated x-values.
In given table we see that there i no repeating x-value. That's why the given table represents function.
Ans(b):
We know that a function can't have repeated x-values.
So if in given table we see any repeating x-value then that may cause the given data set to not be a function.
like if we have 3, 4, 3, 11 in the input then it will not be a function.
Ans(c):
we can use two points say (3,5) and (4,7) to find the linear equation of the form y=mx+b
slope is given by
Noow plug value of m=2 and any point say (3,5) into y=mx+b
5=2(3)+b
5=6+b
-1=b
now plug m=2 and b=-1 in y=mx+b, we get y=2x-1
Hence required equation in function notation can be written as
f(x)=2x-1.
Now to prove that above function is correct, we just graph the given points from table and the obtained function.
We see that points lie on the grpah of f(x)=2x-1.
Which proves that our equation is correct.
For no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.
We have the system of equations:
x + y + z = 2 …(1)
a x + b y + c z = 10 …(2)
x - 2 y + z = 4 …(3)
a. The system has no solution.
Put a = b = c = -1 in (2)
We get:
- x - y - z = 10
Now add (1) and (2)
0 = 12
which is not possible.
So, no solution.
b. The system has exactly one solution.
a = 1 and b = c = 0
We have the equations as:
x + y + z = 2 …(1)
x = 10 …(2)
x - 2 y + z = 4 …(3)
c. The system has infinitely many solutions.
a = b = c = 5
We will have the equations:
x + y + z = 2 …(1)
5 x + 5 y + 5 z = 10 …(2)
x - 2 y + z = 4 …(3)
Therefore, we get that, for no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.
Lear more about system of linear equations here:
brainly.com/question/14323743
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Answer:
its the third one 60,60,60 angles in a triangle add up to 180 degrees 60+60+60=180
Answer:
the correct answer is 3.
Step-by-step explanation:
3×3×3= 27