Answer:
6a^3+ 22a^4+ 14a-10
Step-by-step explanation:
6a^3 10a^2 12a^2 20a -6a -10
Answer18:
The quadrilateral ABCD is not a parallelogram
Answer19:
The quadrilateral ABCD is a parallelogram
Step-by-step explanation:
For question 18:
Given that vertices of a quadrilateral are A(-4,-1), B(-4,6), C(2,6) and D(2,-4)
The slope of a line is given m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
Now,
The slope of a line AB:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{6-(-1)}{(-4)-(-4)}](https://tex.z-dn.net/?f=%5Cfrac%7B6-%28-1%29%7D%7B%28-4%29-%28-4%29%7D)
m=![\frac{7}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B0%7D)
The slope is 90 degree
The slope of a line BC:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{6-6}{(-4)-(-1)}](https://tex.z-dn.net/?f=%5Cfrac%7B6-6%7D%7B%28-4%29-%28-1%29%7D)
m=![\frac{0}{(-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B0%7D%7B%28-3%29%7D)
The slope is zero degree
The slope of a line CD:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{(-4)-6}{2-2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-4%29-6%7D%7B2-2%7D)
m=![\frac{-10}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B-10%7D%7B0%7D)
The slope is 90 degree
The slope of a line DA:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{(-1)-(-4)}{(-4)-(2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-1%29-%28-4%29%7D%7B%28-4%29-%282%29%7D)
m=![\frac{3}{-6}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B-6%7D)
m=![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
The slope of the only line AB and CD are the same.
Thus, The quadrilateral ABCD is not a parallelogram
For question 19:
Given that vertices of a quadrilateral are A(-2,3), B(3,2), C(2,-1) and D(-3,0)
The slope of a line is given m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
Now,
The slope of a line AB:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{2-3}{3-(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B2-3%7D%7B3-%28-2%29%7D)
m=![\frac{-1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B5%7D)
The slope of a line BC:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{(-1)-2}{2-3}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-1%29-2%7D%7B2-3%7D)
m=![\frac{-3}{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B-1%7D)
m=3
The slope of a line CD:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{0-(-1)}{(-3)-2}](https://tex.z-dn.net/?f=%5Cfrac%7B0-%28-1%29%7D%7B%28-3%29-2%7D)
m=![\frac{-1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B5%7D)
The slope of a line DA:
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{3-0}{(-2)-(-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3-0%7D%7B%28-2%29-%28-3%29%7D)
m=3
The slope of the line AB and CD are the same
The slope of the line BC and DA are the same
Thus, The quadrilateral ABCD is a parallelogram
Answer:
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
Step-by-step explanation:
For any angle
, we have that:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
Quadrant:
means that
is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![\frac{1}{16} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\cos{\theta})^{2} = 1 - \frac{1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{16-1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B16-1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{15}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B15%7D%7B16%7D)
![\cos{\theta} = \pm \sqrt{\frac{15}{16}}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B15%7D%7B16%7D%7D)
Since the angle is in the first quadrant, the cosine is positive.
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
I think 2401...I just asked Siri
For A) u must start at -3 on y lines. Then move points up 1 and 3 to the right. Makes point and continue to make lines
For B) start at 5 on y lines, and remember -x is same thing is -1. And negative means go down! So move 1 down and 1 to the right and make point then move 1 down and make 1 right and make second points and continue. Draw a lines.
The solution is when u see two lines from two equations crosses to each other. There’s solution shown.