Answer:
A. Line segment
Step-by-step explanation:
A line segment is measurable because it goes from point A to point B. So thus, answer A is correct.
Hope this helps!!
Answer:
75
Step-by-step explanation:
x is the exterior angle of triangle BDH, meaning that the if you add up the other two angles of triangle BDH, which are the opposite interior angles of angle x, you will get x, which is 75.
If you want to visualize the exterior angle theory, you can look at an example in the picture in this post.
Hope this answer helps you, and was deserving of a Brainiest answer. :)
Answer
Subtract
from ![-2x^2 -15xy+9y^2](https://tex.z-dn.net/?f=-2x%5E2%20-15xy%2B9y%5E2)
then;
![-2x^2 -15xy+9y^2 - (7x^2 -5xy+8y^2)](https://tex.z-dn.net/?f=-2x%5E2%20-15xy%2B9y%5E2%20-%20%287x%5E2%20-5xy%2B8y%5E2%29)
Remove the bracket we have;
![-2x^2 -15xy+9y^2 - 7x^2 + 5xy - 8y^2](https://tex.z-dn.net/?f=-2x%5E2%20-15xy%2B9y%5E2%20-%207x%5E2%20%2B%205xy%20-%208y%5E2)
Like terms are those terms which have same variable to the same power.
Combine like terms;
![-9x^2 -10xy+y^2](https://tex.z-dn.net/?f=-9x%5E2%20-10xy%2By%5E2)
Therefore, Subtracting
from
we get ![-9x^2 -10xy+y^2](https://tex.z-dn.net/?f=-9x%5E2%20-10xy%2By%5E2)
The directions are fairly straightforward. They are asking you to plot the two curves on a graph and find the coordinates of the point of intersection.
After 7 years, the number of birds of each species during that year will be 140.
Answer:
The solutions to the system of the equations by the elimination method will be:
![x=2,\:z=-1,\:y=2](https://tex.z-dn.net/?f=x%3D2%2C%5C%3Az%3D-1%2C%5C%3Ay%3D2)
Step-by-step explanation:
Given the system of the equations
![2x\:+\:2y\:+z\:=\:7](https://tex.z-dn.net/?f=2x%5C%3A%2B%5C%3A2y%5C%3A%2Bz%5C%3A%3D%5C%3A7)
![-x-\:y\:+z\:=\:-5](https://tex.z-dn.net/?f=-x-%5C%3Ay%5C%3A%2Bz%5C%3A%3D%5C%3A-5)
![x+3y-4z=12](https://tex.z-dn.net/?f=x%2B3y-4z%3D12)
solving the system of the equations by the elimination method
![\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2B2y%2Bz%3D7%5C%5C%20-x-y%2Bz%3D-5%5C%5C%20x%2B3y-4z%3D12%5Cend%7Bbmatrix%7D)
![\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3A%7D-x-y%2Bz%3D-5%5Cmathrm%7B%5C%3Aby%5C%3A%7D2%5C%3A%5Cmathrm%7B%3A%7D%5C%3A%5Cquad%20%5C%3A-2x-2y%2B2z%3D-10)
![\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2B2y%2Bz%3D7%5C%5C%20-2x-2y%2B2z%3D-10%5C%5C%20x%2B3y-4z%3D12%5Cend%7Bbmatrix%7D)
![-2x-2y+2z=-10](https://tex.z-dn.net/?f=-2x-2y%2B2z%3D-10)
![+](https://tex.z-dn.net/?f=%2B)
![\underline{2x+2y+z=7}](https://tex.z-dn.net/?f=%5Cunderline%7B2x%2B2y%2Bz%3D7%7D)
![3z=-3](https://tex.z-dn.net/?f=3z%3D-3)
![\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2B2y%2Bz%3D7%5C%5C%203z%3D-3%5C%5C%20x%2B3y-4z%3D12%5Cend%7Bbmatrix%7D)
![2x+6y-8z=24](https://tex.z-dn.net/?f=2x%2B6y-8z%3D24)
![-](https://tex.z-dn.net/?f=-)
![\underline{2x+2y+z=7}](https://tex.z-dn.net/?f=%5Cunderline%7B2x%2B2y%2Bz%3D7%7D)
![4y-9z=17](https://tex.z-dn.net/?f=4y-9z%3D17)
![\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2B2y%2Bz%3D7%5C%5C%203z%3D-3%5C%5C%204y-9z%3D17%5Cend%7Bbmatrix%7D)
Rearranging the equations
![\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2B2y%2Bz%3D7%5C%5C%204y-9z%3D17%5C%5C%203z%3D-3%5Cend%7Bbmatrix%7D)
solve
for z:
![z=-1](https://tex.z-dn.net/?f=z%3D-1)
![\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D4y-9z%3D17%5Cmathrm%7B%5C%3Aplug%5C%3Ain%5C%3A%7Dz%3D-1)
solve
for y:
![4y-9\left(-1\right)=17](https://tex.z-dn.net/?f=4y-9%5Cleft%28-1%5Cright%29%3D17)
![4y+9=17](https://tex.z-dn.net/?f=4y%2B9%3D17)
![4y=8](https://tex.z-dn.net/?f=4y%3D8)
![y=2](https://tex.z-dn.net/?f=y%3D2)
![\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D2x%2B2y%2Bz%3D7%5Cmathrm%7B%5C%3Aplug%5C%3Ain%5C%3A%7Dz%3D-1%2C%5C%3Ay%3D2)
solve
for x:
![2x+2\cdot \:2-1=7](https://tex.z-dn.net/?f=2x%2B2%5Ccdot%20%5C%3A2-1%3D7)
![2x+3=7](https://tex.z-dn.net/?f=2x%2B3%3D7)
![2x=4](https://tex.z-dn.net/?f=2x%3D4)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the solutions to the system of the equations by the elimination method will be:
![x=2,\:z=-1,\:y=2](https://tex.z-dn.net/?f=x%3D2%2C%5C%3Az%3D-1%2C%5C%3Ay%3D2)