Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
Answer:
The jeweler made 9 necklaces.
The jeweler made 8 bracelets.
Step-by-step explanation:
x = number of bracelets
y = number of necklaces
17 = x + y
238 = 5x + 22y
Make one of the coefficients, x, the same.
17 = x + y
Multiply this equation by 5.
85 = 5x + 5y
Subtract the equations to get rid of x.
(238 = 5x + 22y) - (85 = 5x + 5y)
(5x - 5x) + (22y - 5y) = 238 - 85
22y - 5y = 238 - 85
17y = 153
y = 153/17 = 9
The jeweler made 9 necklaces. Substitute this back into one of the equations to find x.
17 = x + y
17 = x + 9
17 - 9 = x
x = 8
238 = 5x + 22y
238 = 5x + 22(9)
238 = 5x + 198
238 - 198 = 5x
40 = 5x
x = 40/5
x = 8
The jeweler made 8 bracelets.
Answer:
Up up up up up up up up up up
Answer:
1/8, 0.35, 0.39, 5/7, 9/10
Step-by-step explanation:
1/8 = 0.125
5/7 = 0.714
0.350
0.390
9/10 = 0.900
now let's order them from least to greatest:
0.125 , 0.350 , 0.390 , 0.714 , 0.900
= 1/8, 0.35, 0.39, 5/7, 9/10
if you have trouble with these types of problems change them all into decimals which will make things easier!
:D
Given:
The system of equations is:
Line A: 
Line B: 
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Equating (i) and (ii), we get
Divide both sides by 2.
Substituting 
in (i), we get
The solution of system of equations is (-4,-8).
Now verify the solution by substituting 
in the given equations.
This statement is true.
Similarly,
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
