15:33
(Mark me the brainliest)
Answer:
Quotient ( x² -4x +10)
Reminder -2
Step-by-step explanation:
We have to consider the polynomial function g(x) = x³ - 3x² + 6x + 8
Now, we have to divide g(x) by (x+1)
Let us arrange the terms of g(x) to get (x+1) as common.
x³ - 3x² + 6x + 8
= x³ +x² -4x² -4x +10x +10 -2
= x² (x +1) -4x (x +1) +10 (x +1) -2
= (x +1)( x² -4x +10) -2
Hence, if we divide g(x) by (x +1) then the quotient will be ( x² -4x +10) and the reminder will be -2. (Answer)
Congruent to angle 1: 3, 5, 10, 8, and 6
congruent to angle 2: 4, 9, and 7
Step-by-step explanation:
Let the first integer be x
2nd integer = x + 1
3rd integer = x + 2
x + x + 1 + x + 2 = -147
3x + 3 = -147
3x = -147 - 3
3x = -150
x = -150 ÷ 3
x = -50
The three consecutive integers are
-50, -49, -48
First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an
S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d] → Equation (1)
S=an+an−1+an−2+an−3+...+a1
S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d] → Equation (2)
Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)
2S=n(a1+an)
S=n/2(a1+an)
Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
