Answer:
What?
Step-by-step explanation:
Answer:
a= 5 and b=1
Step-by-step explanation:
To solve, we will follow the steps below:
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b - 2
We should note that since it has infinitely many solutions then,

Hence
2/a-b = 3/a+b = 7/3a +b-2
2/a-b = 3/a+b
cross-multiply
3(a-b) = 2( a+b)
open the bracket
3a - 3b = 2a + 2b
collect like term
3a - 2a = 2b + 3b
a = 5b -------------------------------------------(1)
Similarly
3/a+b = 7/3a +b-2
cross-multiply
7(a+b) = 3(3a+b -2)
7a + 7b = 9a + 3b -6
take all the variables to the left-hand side of the equation
7a - 9a+ 7b-3b = -6
-2a + 4b = -6 ---------------------------------(2)
but a = 5b
substitute a= 5b in equation (2) and solve for b
-2(5) + 4b = -6
-10 + 4b = -6
add 10 to both-side of the equation
-10 + 10+ 4b = -6+10
4b = 4
divide both-side of the equation by 4
b = 1
substitute b= 1 in equation (1)
a = 5b
a =5(1)
a=5
Therefore, a= 5 and b=1
ax^2 + bx+c =0
discriminant b^2-4ac
(-6)^2 - 4(1) *(9)
36-36 = 0
if the discriminant >0 it has 2 real roots
= 0 it has 1 root of multiplicity 2
< 0 has 2 imaginary root
x^2 - 6x + 9 = 0
(x-3)(x-3)=0
root is 3 multiplicity 2
Answer : double root real and rational
Answer:
In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.
So we just need to take different pairs of consecutive terms and see if their difference is always the same:
1) The differences are:
32 - 35 = -3
29 - 32 = -3
26 - 29 = -3
So yes, this is an arithmetic sequence and the common difference is -3
2) The differences are:
-23 - (-3) = -20
-43 - (-23) = -20
-63 - (-43) = -20
This is an arithmetic sequence, and the common difference is -20
3) The differences are:
-64 -(-34) = -30
-94 -(-64) = -30
-124 -(-94) = -30
This is an arithmetic sequence and the common difference is -30
4) The differences are:
-40 -(-30) = -10
-50 - (-40) = -10
-60 - (-50) = -10
This is an arithmetic sequence and the common difference is -10
5) The differences are:
-9 - (-7) = -2
-11 - (-9) = -2
-13 - (-11) = -2
This is an arithmetic sequence, and the common difference is -2
6) The differences are:
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
This is an arithmetic sequence, and the common difference is 5.