Answer:
x=2.5, y=-5. (2.5, -5).
Step-by-step explanation:
5y+2(2.5)=-10
5y+5=-10
5y=-10-5
5y=-15
y=-15/5
y=-5
Answer:
Option (A) and (C).
Step-by-step explanation:
Prime polynomial can't be written as a product of lower degree polynomials.
(A)
=8x²-6x-4x-3
=2x(4x-3)-1(4x+3)
Here we can't write the polynomial as a product of lower degree.
Therefore it is a prime polynomial.
(B)
8x²+2x-3
=8x²+6x-4x-3
=2x(4x+3)-1(4x+3)
=(4x+3)(2x-1)
Therefore it is not a prime polynomial.
(C)
8x²-6x-3
Therefore it is a prime polynomial.
(D)
8x²+23x-3
=8x²+24x-x-3
=8x(x+3)-1(x+3)
=(x+3)(8x-1)
Therefore it is not a prime polynomial.
Answer:
T = 8 + 5 + 6
Step-by-step explanation:
Since it took Penelope 8 minutes to drive to the store at a rate of 1 block per minute then that means the store was 8 blocks away. That being the case if she drives back home from the store at 4 blocks every 3 minutes that would mean that she took 6 minutes (4+4 = 8) to get back home. Using this data we can create the following equation model to calculate the total time of the trip.
T = 8 + 5 + 6
F(x)=x⁴-1
f'(x)=4x³
Newton’s Method: x[n+1]=x[n]-f(x[n])/f'(x[n]); x[n+1]=x[n]-(x[n]⁴-1)/4x[n]³
x₁=3.00390625
x₂=2.26215...
x₃=1.7182...
X'=X-(X⁴-1)/4X³=X-X/4+1/4X³ is a symbolic way of writing the recursive formula, where X' represents the next iteration.
When X'≈X, -X/4+1/4X³≈0; so X/4≈1/4X³; X≈1/X³, so X⁴≈1 and X⁴-1≈0. But this is f(x)≈0. Hence Newton’s Method converges to a solution.
The rate of change is x[n+1]-x[n]=-(x[n]⁴-1)/4x[n]³=x[n]/4-1/4x[n]³ or symbolically -X/4+1/4X³.
Note that the method converges to one solution. A different x₀ will possibly converge to the solution x=-1.
