Write out all the pairs of numbers which can be multiplied to produce c.
Add each pair of numbers to find a pair that produce b when added. ...
If b > 0, then the factored form of the trinomial is (x + d )(x + e). ...
Check: The binomials, when multiplied, should equal the original trinomial.
She has a 50 percent chance she flips the coin on tails.
I guess you want to find the average speed for the whole journey
average speed = distance travelled / time
the distance from home to the shop = speed * time = 0.5*10 = 5 miles
time for travelling back = distance / speed = 5/30 = 1/6 hours
average speed for whole journey = 10 / (1/2 + 1/6) = 10 * 3 / 2 = 15 mph
The n-th term is given by
![a_n=a_1\cdot r^{(n-1)}\qquad\text{where r is the common ratio}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7B%28n-1%29%7D%5Cqquad%5Ctext%7Bwhere%20r%20is%20the%20common%20ratio%7D)
Then we can find the common ratio from the given terms.
![\dfrac{a_4}{a_1}=\dfrac{a_1\cdot r^{(4-1)}}{a_1}=r^3=\dfrac{-16}{1024}=\left(\dfrac{-1}{4}\right)^3\\\\r=\dfrac{-1}{4}\\\\a_6=1024\left(\dfrac{-1}{4}\right)^5=-1](https://tex.z-dn.net/?f=%5Cdfrac%7Ba_4%7D%7Ba_1%7D%3D%5Cdfrac%7Ba_1%5Ccdot%20r%5E%7B%284-1%29%7D%7D%7Ba_1%7D%3Dr%5E3%3D%5Cdfrac%7B-16%7D%7B1024%7D%3D%5Cleft%28%5Cdfrac%7B-1%7D%7B4%7D%5Cright%29%5E3%5C%5C%5C%5Cr%3D%5Cdfrac%7B-1%7D%7B4%7D%5C%5C%5C%5Ca_6%3D1024%5Cleft%28%5Cdfrac%7B-1%7D%7B4%7D%5Cright%29%5E5%3D-1)
The appropriate choice is -1.