Answer:
Step-by-step explanation:
Answer:
steps below
Step-by-step explanation:
x⁶ - 7x³ - 8 = (x⁶ + x³) - (8x³ + 8)
= x³ (x³+1)-8(x³+1)
= (x³ - 2³)(x³ + 1)
= (x-2)(x²+2x+4)(x+1)(x²-x+1)
(x-2)(x²+2x+4)(x+1)(x²-x+1) = 0
<u>x= -1 or x = 2</u> ... roots
or x²+2x+4=0 or x²-x+1=0
x²+2x+4=0
x = (-2±√4-16)/2 = <u>-1 ± √3 i</u> ... complex roots
x²-x+1=0
x = (1±√1-4)/2 = <u>1/2 ± (√3)i / 2</u> ... complex roots
<u />
b) P(x) = x⁶ - 7x³ - 8
= <u>(x-2)(x²+2x+4)(x+1)(x²-x+1)</u>
= (x+1)(x-2)(x-(-1 + √3 i))(x-(-1 - √3 i)(x-(1/2 + (√3)i / 2))(x-(1/2 - (√3)i / 2))
Answer:
N(h) = 2h + 6
Step-by-step explanation:
A model of the number of people that Denis can invite to his party:
N(x) = x/25.............(1)
Where x = amount of money saved
Amount of money saved can be modeled by the equation:
M(h) = 50h + 150...........(2)
In the above model, h = number of overtime hours
M(h) = amount of money saved = x
Therefore equation (1) can be re - written as:
N(x) = M(h)/25.................................(3)
Substituting equation (2) into equation (3)
Find an explicit expression that models the number of people that Denis can invite to his party if he worked h overtime hours this week can be expressed as:
N(h) = 2h + 6
Answer:
f(x) approaches positive infinity.
g(x) approaches negative infinity.
the y-intercept of f(x) is less than the y-intercept of g(x).
Step-by-step explanation:
the highest power of x in f(x) is 3, and it has a positive sign. so, the bigger x the more the x³ part will dominate.
therefore, with x going to positive infinity, also f(x) goes to positive infinity.
the graph of g(x) clearly dives down never to come back up or flatten out. so, with x going to positive infinity, g(x) goes to negative infinity.
the y-intercept of f(x) = f(0).
that means the functional value when x=0.
so, for x=0 this means
y = 2×0³ - 3×0² + 5×0 + 7 = 7
the graph of g(x) shows that g(0) is 8.
so f(0) is less than g(0).
