Answer:
Let p(x) = x3 + ax2 + bx +6
(x-2) is a factor of the polynomial x3 + ax2 + b x +6
p(2) = 0
p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0
7 +2 a +b = 0
b = - 7 -2a -(i)
x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.
p(3) = 3
p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3
11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)
Equating the value of b from (ii) and (i) , we have
(- 7 -2a) = (-10 - 3a)
a = -3
Substituting a = -3 in (i), we get
b = - 7 -2(-3) = -7 + 6 = -1
Thus the values of a and b are -3 and -1 respectively.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The perpendicular lines have opposite reciprocal slopes.
<u>The given line has a slope of:</u>
<u>The perpendicular slope is:</u>
<u>And its y-intercept is:</u>
<u>The line is:</u>
<u>Convert this into standard form and compare with answer choices:</u>
- 3y = 2x + 21
- - 2x + 3y = 21
Correct choice is A
Answer:
value of buyout is $4185.74
Step-by-step explanation:
given data
car worth = $25077
down payment = $3560
monthly payment = $336 = 336 × 6 = $2016 per semi annually
time = 5 year = 10 half yearly
rate = 4.04 %
to find out
value of final buyout
solution
we know here loan amount will be 25077 - 3560 = $21517
and we find present value first by formula that is
present value = 
put here t = 10 and r = 
so
present value = 
present value = 18089.96
so
loan unpaid amount is here
loan unpaid amount = 21517 - 18089.96
loan unpaid amount = $3427.04
so
now we calculate value of buyout
that is express as
amount = principal × 
amount = 3427.04 × 
amount = 4185.74
so value of buyout is $4185.74
We can get two different equations from this:
3x = 18
and
3x = -18
So:
x = 6, x = -6
x = {6, -6}