Answer:
![5b^2(x-0.2)(x+3)](https://tex.z-dn.net/?f=5b%5E2%28x-0.2%29%28x%2B3%29)
Step-by-step explanation:
The first thing that I noticed was that all of the terms had a common factor of
. You can therefore factor that out first:
![5x^2b^2 + 14xb^2 -3b^2= \\\\b^2(5x^2+14x-3)](https://tex.z-dn.net/?f=5x%5E2b%5E2%20%2B%2014xb%5E2%20-3b%5E2%3D%20%5C%5C%5C%5Cb%5E2%285x%5E2%2B14x-3%29)
Now, you have a quadratic equation inside the parentheses. Factoring, you find that the roots are -0.2 and 3, meaning that you can further factor this expression to be:
![5b^2(x-0.2)(x+3)](https://tex.z-dn.net/?f=5b%5E2%28x-0.2%29%28x%2B3%29)
Hope this helps!
The number of terms in the binomial expansion of (3x-5)^9 is 10
Answer:
4160 cubic inches
Step-by-step explanation:
The dog carrier is in the shape of a rectangular prism (cuboid).
The volume of a rectangular prism is given as:
V = L * W * H
where L = length, W = width, H = height
The carrier is 20 inches long, 13 inches wide, and 16 inches high.
Therefore, its volume is:
![V = 20 * 13 * 16\\V = 4160 in^3](https://tex.z-dn.net/?f=V%20%3D%2020%20%2A%2013%20%2A%2016%5C%5CV%20%3D%204160%20in%5E3)
The volume of the dog carrier is 4160 cubic inches.
Answer:
B. ![B = (4,-2)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C-2%29)
Step-by-step explanation:
GIven that
and
, and that point M is the midpoint of AB, the midpoint can be determined as a vectorial sum of A and B. That is:
![M = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20A%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20B)
The location of B is now determined after algebraic handling:
![\frac{1}{2}\cdot B = M - \frac{1}{2}\cdot A](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20B%20%3D%20M%20-%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20A)
![B = 2\cdot M -A](https://tex.z-dn.net/?f=B%20%3D%202%5Ccdot%20M%20-A)
Then:
![B = 2\cdot (1,0)-(-2,2)](https://tex.z-dn.net/?f=B%20%3D%202%5Ccdot%20%281%2C0%29-%28-2%2C2%29)
![B = (2\cdot 1, 2\cdot 0)-(-2,2)](https://tex.z-dn.net/?f=B%20%3D%20%282%5Ccdot%201%2C%202%5Ccdot%200%29-%28-2%2C2%29)
![B = (2,0) -(-2,2)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C0%29%20-%28-2%2C2%29)
![B = (4,-2)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C-2%29)
Which corresponds to option B.
13 + 3i
15 - 6i - 2 + 9i → Sum
collect like terms
(15 - 2) + ( - 6i + 9i) =13 + 3i