Answer:
![(x-\frac{1}{4})^{2} \geq \frac{-39}{16}](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%5Cgeq%20%5Cfrac%7B-39%7D%7B16%7D)
Step-by-step explanation:
Rewrite into standard form:
![2x^{2} -x+5 \geq 0](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20-x%2B5%20%5Cgeq%20%200)
Complete the square:
![2(x-\frac{1}{4} )^{2} + \frac{39}{8} \geq 0](https://tex.z-dn.net/?f=2%28x-%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7B2%7D%20%2B%20%5Cfrac%7B39%7D%7B8%7D%20%5Cgeq%200)
Subtract
from both sides:
![2(x-\frac{1}{4})^{2} \geq \frac{-39}{8}](https://tex.z-dn.net/?f=2%28x-%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%5Cgeq%20%5Cfrac%7B-39%7D%7B8%7D)
Divide both sides by 2:
![(x-\frac{1}{4})^{2} \geq \frac{-39}{\frac{8}{2}}](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%5Cgeq%20%5Cfrac%7B-39%7D%7B%5Cfrac%7B8%7D%7B2%7D%7D)
Simplify:
![(x-\frac{1}{4})^{2} \geq \frac{-39}{16}](https://tex.z-dn.net/?f=%28x-%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%5Cgeq%20%5Cfrac%7B-39%7D%7B16%7D)
Answer:
270,000,000,000
Step-by-step explanation:
It is misleading because the points on the x-axis are not in the same unit. The years should be numbered the same units.(:
You can stack the eight books on top of each other is one way. And then you can changed the order of how you stack the book 64 different ways. You can also do this vertically standing up. With the spin of the book facing in or out. You can arrange the. By height, color, alphabetically, thickness, year published... basically any individual characteristic they can have can be a way you stack a book.
The first thing you need to do is multiply the a and c values. in this problem a is 3 and c is 4. 3x4 is 12. now you need to find the factors of 12 and find a set that add to the b value (-8). -2 + -6 is -8 and -2 x -6 is 12. now you replace -8x with -2x and -6x. now you need to factor by grouping. so first is 3x^2 -6x. you factor out the gcf between the two. in this case it us 3x. so now you have 3x(x-2). now you need to factor the other side of the equation (-2x +4). for this problem you need to factor out a -2, rather then 2, because it needs to be the same as the first half. so you factor out the -2 and get -2(x-2). then you just combine the two so you get (3x-2)(x-2). hope this helped. i also attached a picture of the work. :)