Answer:
the blue dot is at -11 value on the number line.
Answer: x = 0
y = 2
z = -1
Step-by-step explanation:
The system of equations are
x+y+z=1 - - - - - - - - - - 1
-2x+4y+6z=2 - - - - - - - - - 2
-x+3y-5z=11 - - - - - - - - - 3
Step 1
We would eliminate x by adding equation 1 to equation 3. It becomes
4y -4z = 12 - - - - - - - - - 4
Step 2
We would multiply equation 1 by 2. It becomes
2x + 2y + 2z = 2 - - - - - - - - - 5
We would add equation 2 and equation 5. It becomes
6y + 8z = 4 - - - - - - - - - 6
Step 3
We would multiply equation 4 by 6 and equation 6 by 4. It becomes
24y - 24z = 72 - - - - - - - - 7
24y + 32z = 16 - - - - - - - - 8
We would subtract equation 8 from equation 7. It becomes
-56z = 56
z = -56/56 = -1
Substituting z = -1 into 7, it becomes
24y - 24×-1 = 72
24y + 24 = 72
24y = 72 - 24 = 48
y = 48/24 = 2
Substituting y = 2 and z = -1 into equation 1, it becomes
x + 2 - 1 = 1
x = 1 - 1 = 0
Answer:the 57th term is 78
Step-by-step explanation:
The sequence is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = - 6
d =3/2
n = 57
We want to determine the value if the 57th term, T57. Therefore,
T57 = - 6 + (57 - 1) ×3/2
T57 = - 6 + 56 × 3/2 = - 6 + 84
T57 = 78
would represent the slope of this line (also known as the gradient of this line,) whereas
would be the
-intercept of this line.